You actually won't need any i.d. for her even if she does have her own seat on the plane. My kids are 12 and 3 1/2 years old, and they have never needed i.d. for the plane, just my husband and myself. If we travel outside of the U.S. then we all need passports for that.
I know that in the past when my dd was 2 years old, she was very tall for her age, and most people thought she was over 3 years old, so I was concerned that they would ask for a ticket for her at the gates, since she looked like she was over 3 years old, so we brought her birth certificate or passport with us, just in case they asked. When we were dining a few times they asked us if she was 3 years old, so they could charge her the child's price, but when I told them she was only 2 they said ok, and didn't ask for proof of age. I had it with me just in case. We didn't want any problems.
