Re: flying with a 3mo old?
If I were in your shoes, I would check the car seat (well padded) and simply carry your baby. The first time we flew, we just used a carrier, but I had my husband to lug our carry ons. The 2nd time, I was alone, and I was glad for the stroller (that I gate checked) so I could wear my baby and put my heavy old backpack in the stroller. Bonus - you CAN wear your baby through security in a carrier - so, so much easier. They just have to do a quick swab of your hands afterward to make sure you don't have explosive residue on them.
Also, bring shot records or a birth certificate copy so you can verify her age. Some airlines are picky about this even if the baby isn't even remotely close to 2 years of age!