
Hi! Don't worry, the advice given will be the same no matter how many dogs anyone has because you can never stop learning! :)
In a way your vet is right, that your puppy will let you know when it's tired, but you do have to know what signs to look for. Like children, they'll keep going as long as possible, way past the time they should rest, and then they get overtired and grumpy, and can do themselves harm. So to start off with keep the walks short - the general rule of thumb for the average breed is 5 minutes formal exercise per month of age - so a three month pup would get walks of about 15 minutes, which to start with is generally plenty. At this stage they're not being walked for exercise (they get plenty of that playing at home and in the garden) but more for socialisation and training. Of course yours is a small puppy so you'll be able to pick him up and carry him when necessary - owners of other breeds don't have that luxury and have to time their walks carefully!
As long as he has plenty of rest between his outings I'm sure he'll be fine.
:)