Sweatpeas, you have found the right place. I am not in the US, so someone else will have to answer your education questions for you, but I wanted to say welcome!

And no, a child as advanced as your DD is at 16 months is highly unlikely to level out by grade 3. If she is PG (which she sounds) then she is as different from an MG kid as an MG kid is from normally developing, a typical gifted program will not be targeted at at her needs. And the early years of school before, your local public gifted programs start, when all the other kids are figuring out the alphabet, reading and counting will likely throw her difference into particularly stark contrast. I would say your paed was right to warn you to start thinking now!