For a first birthday, be sure to make it at a time when her daughter won't be tired/sleepy and not during her naptime, of course. We did ours as a breakfast for my son, and everyone loved it. We thought it would be very small, since it was early (10 a.m.), but nearly everyone showed up and the place was full. The area where my son stayed was a smaller area; so, he didn't get overwhelmed with the noise. Everyone else was in another area with the kids playing. (This was at Tumbleweeds 4 years ago.) Anyway, everyone had a great time. It was privately rented; so, only our kids were there. And the facility had employees that helped and made sure none of the kids left. It made socializing with family/friends very relaxing, and the kids enjoyed their play time.
If she doesn't want to go with the usual character themes, then what about a seasonal theme (Winter Wonderland), where there could be activities and decorations that the kids would like and relate to. One activity could include something like decorating your own snowman cupcake. Give the kids a cupcake and plate with a little bit of frosting to frost the cupcake with. On the plate, also have some different candies to make a nose (candy corn), eyes (M&Ms), mouth (string licorice), ear muffs (gum drops and string licorice). Skip the candy for the birthday child's and just let her eat the cupcake. :)
If you want some more ideas, let me know. I don't want to take up your whole screen. lol Best wishes to you!