There are some limits (e.g., size, materials), but paper doll or pre-assembled puzzle both sound lovely for your little girl, so long as it fits within the size guidelines, which I think is a 9x12 envelope less than 1/4" thick. This thread might be helpful:
Hi Scott! Welcome to the Compassion support community! That is very thoughtful of you to want bless your child with a gift to open for her birthday and, I agree with Debi, those both sound like great ideas for things to send to your sponsored child as a gift! One note on the paper dolls, I know that it's fine to laminate those so that they last longer in case you had wondered about that. I don't usually laminate the ones I send but I've seen that question come up on here a time or two. Also, like Debi mentioned, the puzzles should be pre-assembled and I've sent those before wrapped in clear plastic wrap with a thin piece of cardboard in between the two sides. You might also wrap some bands of clear packing tape around it just for added strength. I have had one puzzle come apart at the hands of the USPS before. :) Some other ideas might be matching games or Uno cards or other card games. Peaceable Kingdom makes all kinds of stuff like that. There really is all kinds of things you are able to send. Basically the only guidelines are that it be made of paper and no larger than 8-1/2" x 11" and 1/4" thick. In addition to the forum that Debi linked to there is an article here that might give you some more ideas about what Compassion is able to send. It really is fun to send things like that to our kids! I know that your girl is just going to be thrilled with whatever you decide to send her for her birthday! If you have any more questions about anything please don't hesitate to ask.