Most trainers will tell you that waiting until your older dog is at least 18 months or older before getting a second pup makes sense. You want the training and maturity of your older dog to be stable before introducing a new pup. Often, a family enjoys their first pup so much that they get a second one too soon, causing the older pup to regress in training and behavior as the focus is less on him/her and more on the new pup. I agree with the trainers on this one. You worked hard to get your older pup trained and on a schedule that works for both of you and don't want to mess that up and make life harder for yourself needlessly.
On the other side of the age issue, I think it makes sense to get your second dog while your older one is still very active and energetic. The ideal time would be when the older dog is between 18 months and three years or so. This way, the dogs can enjoy each other's company for a good chunk of years with the same or similar aging time table.
Speaking of enjoying each other's company, please realize that this isn't guaranteed to happen. In fact, my two Labs aren't bosom buddies. Casco, my older Lab, tolerates Tonya and not much beyond that. Many people think they'll be doing their older dog a big favor by getting him or her a playmate or friend and they are greatly dismayed when the two dogs don't become BFFs. Often, in an effort to "make" the dogs get along, humans will step into the relationship and reprimand the older dog for being "mean" to the younger one. If your older dog is truly a social dog who greatly enjoys the company of other dogs, it's more likely that s/he and a second dog will get along and play well together. If your older dog could take or leave other dogs, is more interested in being a companion to YOU, and/or has not been well-socialized as a pup, chances aren't so great that s/he will form a close, playful bond with a new addition to the family.
In my case, I knew my older Lab (two years old at the time) was a HUGE fan of people but was dominant around other males and had an aloof personality. Our decision to bring a second Lab into our home was based on a desire to be of service to a non-profit service dog agency. We understood that we would be fostering a puppy for a couple of years and participating in a rigorous training program with her. She would be away at "school" on weekdays being trained at the training center. We thought this would be a good chance for us to see how Casco would do with a second dog without it necessarily being "forever." Casco remained his aloof, standoffish self throughout the first year while Tonya was a pup. Tonya is very sweet-natured and really wanted to be Casco's best friend and cuddle buddy. He would have NONE of this. In fact, he would "yell" at her if her paw even touched him while they were sleeping. Sigh.
Tonya ended up being "ours" in the end, after she was released from the program due to health issues at 18 months of age. Our two Labs have never once fought with each other. They've simply worked out a relationship based on Casco's boundaries and limits. Despite being the same breed, they are two entirely different dogs in every way. He's an American Lab - tall and lanky with a huge head and long snout. He's hyper and bull-headed. If you ask him for some love, he'll go and get his tug toy. She is an English Lab - short and stocky with a block head and a short snout. She's mellow and sweet-natured and would never think of jumping on a human. She's happy to lie by your side and have her belly rubbed and her forehead kissed. For us, as their owners, we've learned to respect the relationship they've worked out. Yes, Tonya would've loved to have a housemate with whom she could share a bed every night for an eight-paws-entwined cuddlefest. Yes, Casco would've loved to shove her right back out the door on the very first day we brought her home. In the end, we've got two fantastic individual dogs who tolerate each other with respect and who occasionally run around in the field together and wrestle....as long as Casco ALWAYS wins.
Casco has always been very independent and totally trustworthy with the full run of the house from about six months of age. Tonya is more fearful and has a lot of concerns, so it turns out that Casco has been the perfect "babysitter" for her. I think she'd be a dog with some anxiety and separation issues if it weren't for her solid, predictable older bro keeping track of her while we're working or away for a few hours. Casco's never been one to cuddle with us and he gladly handed that nightly duty over to his younger sis. He watches with a look of semi-disgust on his face from his cushy corner dog bed while Tonya lounges on her back our bed pillows while we watch TV and pet and kiss her each night before sleep. So...they've worked it out and we've worked it out so that everybody gets their needs met for the most part.
Three DWD families have brought a second pup into their homes this spring, and another family is expanding in July. In the case of Lucy Bedlington Terrier (about 2 years old), her human mom's choice of another female Bedlington as a baby sis for Lucy is working out amazingly well. Lucy is proving to be a tolerant, kind and fun older sis. Ivy Rose has a sweet personality and they are playing well together, after about five weeks or so together so far. Brodie Westie's mom chose a female Westie pup as a companion for Brodie (he's about 14 months old). Brodie just loves his little sister, Kaylee, and they play quite well together. Kaylee is more tolerant of and interested in children than Brodie is and we're hoping that Brodie learns that kids aren't so bad from seeing/experiencing his sister's joy at kissing babies and tots. Bailey (about 2.5 years old) is what we affectionately call an "apartment-sized Lab." She is a mixy-mix of who knows exactly what! Her parents rescued a second mixy-mix this winter. The new sis is a female Dachshund/Pekinese mix who is just full of love and energy. Pika, the new pup, has presented some issues that Bailey did not. The parents of these two dogs are very committed to training their dogs well and have sought out both in-home support, 1:1 training sessions at a training center and some specialized classes to suit the needs of their brood.
Last spring, two of my DWD families with female English Bulldogs bought siblings from the same litter, each bringing home a second female E.B. as a companion for their older gals. The integration of these younger bullies into the families has been a bit more of a challenge. The two older Bulldogs, Lola and Mosley, were about two when the younger sisters arrived. Lola and Mosley spent a lot of time together, visiting at each other's homes and spending at least a day each week together here at DWD. Lola was very slow to warm to her new baby sister, Trixie. Recently, Lola has decided she really doesn't care for Mosley's new sister, Charlie, so much either. They get into feisty, violent fights and Charlie has developed some fear around Lola. This is frustrating and challenging for the two families, who had visions of bringing up the four dogs together, sharing responsibility for dog-sitting, etc. At this point, they are considering bringing in a trainer to see if they can do anything about Lola's issues with Charlie.
So...it's a mixed bag, this life with more than one dog in the house. Lots of times, it works out great. Other times, it's an adjustment of small or large scale, depending on the situation. If I had it to do over again, would I have two dogs at the same time? Would I choose the same breeds? I think that people have different needs and wants at different times in their lives. One of my newer customers who has been a Lab owner for years and just switched to an English Cocker as her new companion told me that she recently met a lovely elderly woman (in her 90's?) on a plane and that got to talking about their lives with dogs. This woman had owned all kinds of dogs, all shapes and sizes and temperaments, in her life time. She told my customer that there is a breed for every stage of a person's life. I like that idea.... Maybe my next dog will be a little Schnauzer. Who knows??