Jackson was 9 weeks old when introduced to my moms 4 year old cockapoo, Carmen, and my dads 2 year old JRT mix. I lived with my mom so he had to be around Carmen and we spent an equal amount of time at my dads house. So he was around them from the time he came home! I think it's fine so long as the other dog has it's shots/etc.
I wouldn't do dog parks and pet stores for a few weeks after shots though. But I've always allowed pups (family dogs, etc) to go outside in our yard right away.