You only need FP for the E-tickets. Not Alice or Tea Party - they don't have it anyway. Your best bet if Alice is your priority on your birthday is just head for Fantasyland at rope drop that morning and you should be able to jump right on. Alice can get up to 45 minute waits at high points during the rest of the day but if you keep checking back, you can often find a point to jump in with a 20 minute wait or less. Use FP for the mountains and RSR and Guardians. Hit Fantasyland first thing (Peter Pan and Toad tend to have the longest waits so if you can wait for Alice, do those two first) otherwise. Or New Orleans Square for Pirates and Mansion first thing. But another fun option is to do Mansion last thing at the end of the night before park closing - the atmosphere is great then for the queue.