I made several piñatas like this with my kids when they were younger, and honestly it works great. The technique is simple: you need a balloon as a base (or a cardboard box if you want something sturdier), and then comes the fun part of preparing the paste. You mix flour with water until it's like a liquid batter with no lumps, some people add a bit of salt so it doesn't spoil if it takes you several days. Then you tear newspaper into strips that aren't too small, dip them in the paste and stick them to the balloon layer after layer. The important thing is that each layer dries well before you add the next one, or you end up with a sticky mess. I let it dry between layers for about three or four hours if I can, or if I'm in a hurry I stack them anyway but the whole thing takes longer to dry.
What I discovered after a couple of failed attempts is that if you use old newspaper instead of white newsprint, it looks way better in the end and also absorbs the paste better. And here comes the trick that not everyone knows: before painting the finished piñata, give it a coat of white cardstock glued on with the same paste, like it's just another layer. It saves you a ton of paint and the result looks way neater. For details like ears or a snout if it's an animal, glue on corrugated cardboard or molded papier-mâché before you call it done. After everything is completely dry, you can paint with whatever you have on hand, acrylic paint works perfectly. To fill it with candy, once it's ready you carefully make an opening in the back, fill it, and close it with tape or glue. Your daughter is going to love it knowing you made it especially for her.