We've always done rather frugal parties - life w/ 4 kids is all about budgeting, lol. I used to think I was pretty good at it, until I saw a show on TV about a family w/ 9 kids (12 kids? 14 kids?? - a lot of kids, I forget how many, lol) - and they have one party a year for all the kids and they were going to have 100 people at the party and they only spent $100 on food!! I was so impressed!
Anyhow, I think you have gotten a lot of great suggestions! 3 year olds are easy to entertain, and they're great at simply playing w/ each other!
When we have parties, I usually set up something small, and most of the time the kids are just running around playing w/ each other.
I usually have a craft table set up w/ glue (or glue sticks for the smaller ones) and pre-cut shapes, paper, stickers, shells, beans, shaped pasta, foam letters, popsicle sticks, etc and let the kids make something. Once or twice it's been themed, like when my dd had all her friends bring dog/cat food to donate to the animal shelter instead of bringing gifts, we did foam animal picture frames.
For food, you can do simple finger foods like chicken nuggets (Tyson frozen dinosaur nuggets are reasonably priced), chips, carrots, canteloupe, grapes, apple slices, cheese quesidillas, sandwiches, mini pizzas, etc.
I love the ideas about making cupcakes or cookies for the kids to decorate. We do that sometimes also. The kids ALWAYS have fun doing that, no matter how old them are!! We prefer to do sugar cookies, simply b/c they can decorate and eat more than one or two w/ me feeling like they really ate too much junk, lol (as opposed to cupcakes where I just would not want them to eat 3 at one sitting!).
Most importantly though (in my humble opinion) just let the kids play and have fun and go w/ the flow. I think sometimes birthday parties become so over the top and parents end up spending a ton of money. I do know a few people who go way out for their kids parties, and really I think it is just too much. We no longer go to those parties b/c they are just too stressful and competitive and all about show.
These days, we and most of our friends have home parties, we invite lots of kids and everyone in their family and we always have so much fun just hanging out w/ each other and the kids have so much fun playing!
Good luck to you, hope she has a great party! How fabulous she was blessed w/ the gift of a new heart and parents who love her! God Bless!