
Personally, I would wait until your dog is at least two and has fully matured and grown out of the "teenage" behaviour which you may be about to experience in the new few months!
I recently (September) got a second dog and went for a male (having already got a female) as various people told me that dogs of different sexes are more likely to get on. Having said that, there are plenty of people on this forum with multiple dogs, and they clearly get on fine. My older dog hated the puppy at first - she sulked for weeks, and really disliked all the jumping, running around and nipping he did (and who can blame her?). She tolerates him much better now that he is a bit more civilised, but I don't think they're ever going to be best friends or curl up in a basket together. I understand that male dogs are generally not keen on puppies, so it would probably be worth organising separate spaces for them initially. My pup still has a pen (he's six months old) that he can be removed to if he gets overexcited. Without that, things would have been very difficult, and the arguments between the two dogs much worse.
For the first few months, it is very hard work having a pup and an older dog, though I should add that I have a particularly lively breed. The two dogs need to be excerised separately, trained separately, they eat at different times. The puppy obviously takes up a lot of time, but equally the older dog needs much more attention than usual so that it doesn't feel put out. It felt like much more than double the work having two and for quite a while we felt that we'd made a mistake getting the new puppy, but things have calmed down now and there is light at the end of the tunnel.