There is no restaurant that always does something special. It really depends on how busy they are, the CM, etc. That said, at Biergarten they will sing Happy Birthday and mention names during each set. You just have to let them know you are celebrating a birthday when you check in.
We like to order special custom cakes at Disney and are doing so next week for my son's 9th and my 40th. But we picked our location based on where we could order the cakes we wanted. Yes, I'm that much of a cake fanatic, lol. The cake offerings vary by location. They all have the podium cakes and all Disney owned and operated restaurants now have the Mickey Head Celebration Cake which is pretty cool. MK restaurants have a special dessert at each restaurant you can preorder. You can look through the cake thread for more info on those options.
If your daughter has favorite characters or a favorite restaurant or meal you could just pick something that fits that as well. It will be fun no matter what you go with no doubt.