Lele,
First of all congrats!!
We took our daughter (now 13 mos) to Disney for the first time for 3 days/2 nts when she was 2-1/2 months old. We had a wonderful time! It was just me and my DH, the baby and our other DD (5). She pretty much stayed in her stroller/infant seat the whole time sleeping or just staring around. She loved the fresh air and just being outside. I did bring my Baby Bjorn and she was very happy in that. We made sure we just took it easy and explained to our DD that we couldn't do everything. (We never do anyways, we are AP holders, so she is used to us taking our time in the parks.)
As far as rides, we took her on Peter Pan, Buzz, Snow White, etc. I took her on the WDW Railroad a couple of times around while my DD and DH tackled SM and BTMR. It was very relaxing! The rides that she couldn't go on, my DH and I just alternated with my DD. I am a people watcher though, so I enjoyed just hanging out w/ the baby.
We stayed at POR and loved the room (Alligator Bayou). The first night we were there was actually the first time she slept through the night! I took this as a good sign, a true Disney baby!
We did use the baby care center - USE IT, it's wonderful! And we ate a late lunch/early dinner at Columbia Harbor House upstairs. It was empty and we were able to stretch out and relax. I could feed the baby and we all had some down time.
I never got those "I can't believe she has a little baby at Disney World" looks, mostly just oohs and aahs. I did have a few people wanting to touch her, but I just had to say sorry! Stitch did tickle her toes, though!
As far as weather, it will probably still be pretty warm. But just dress the baby cool and you'll be fine. Maybe a blanket in the evenings or bring jammies to change the baby in to.
I don't think we did AK, just MK and MGM. Maybe Epcot, but I would have to look. We have been several times w/ the baby, and we have never had a problem. She is very easygoing, so that probably helps. She loves going now, pointing at Mickey and loves all the lights at night. Honestly, it was easier and more leisurely bringing her when she was a 2-1/2 mos old, b/c now she walks!

But I can't complain, she's good!
Hope this helps you decide! Good luck!