Morning N.,
I totally understand you wanting to do something special for her actual "BIRTH DAY"! I am the same way with my children and they are 8, 5 and 6mns. Yet, I am selfish and don't want to have an actual party for them on that day (unless it falls on a weenkend). What we usually do is just a little cake and ice-cream (or some other healthy choice you may find to use), with just the kids and us. This way they have something special always on their DAY, and we do the parties on the weekend either before or after (which ever is closest to the day).
Shes is only turning one, so making a big deal out of it is more for us parent's benefits and those around us who want to spoil our kids hehe, she won't remember what you end up doing. So good luck with the wedding, but most of all good luck in finding a solution that will work for you and your little one.