It sounds like your puppy has the potential for this!
I'm in the process of having one of my dogs certified right now. He'll be my second therapy dog. It really is a very rewarding experience!
Assuming you want to test and join a specific organization (I highly recommend this as your membership will include insurance just in case something does happen) you will not be able to test until your pup is atleast one year old. Though be sure to check on age requirements before testing as they could vary from one organization to another.
Definitely work towards and earn your CGC first, like Julie suggested. It will give you a really nice head start, not to mention that therapy dog certification tests (atleast those I am familiar with) include most/all of the CGC tests. You may even want to consider trying for your S.T.A.R. Puppy before the CGC if tesing is available in your area.
And IMO the best Therapy Dogs are social, calm, gentle, affectionate, stable, and well trained. Basically a bomb proof dog! There are just so many things from unsteady/shaky movement of the eldery to medical equipment to the unpredictable nature of children that they need to be comfy with.
Here are a few sites for you to look over. If you have any questions feel free to ask! I'll do my best to help out! AKC's Canine Good Citizen (CGC) Program Therapy Dogs International