I agree with the others that you're worrying too much about this. I don't know exactly how your program works, but I know some places take what the child is given and add other things as needed. So if she has siblings, they'll probably make sure all the kids' gifts are comparable.
We pick at least one ornament off our church giving tree every year. Some years, we get a tag with a child's name and a couple specific requests. Other years, we just get a generic "5-year-old boy" or something like that. If the tag has a specific request (toy/clothes), we try to honor it.
This year, we actually picked three tags off the tree -- one to match up with each of my three kids. Each child is getting 1-3 toys/games, a couple books, a new shirt/pants, a pair of socks, hat, and gloves. When I was out shopping for my kids, I'd just pick up a couple similar items for the "giving tree kids," especially if I found a good deal. I figure most families can never have too many hats/gloves/socks since they're always getting lost. (I know we need plenty of extras!) I like tossing in the books, too, because you'd be surprised at how few books some families have. If I had to guess, I'd say we spent about $50 per child, but it may be a bit more than that since I kept tossing in several small items.
As for the race of the doll, don't let it bother you. If you and your daughter think it would be a great gift, then buy it! We have baby dolls of multiple races, and my children all play with them happily. Children don't tend to see skin color as an important difference -- it's just like hair color to them.
Also, keep in mind that if this family is on a giving tree, they don't have much. Odds are that the child won't already have whatever you buy. And if by some small coincidence, she does, she can learn the value of regifting. :-) She also may just be thrilled to have two of the same thing.
Just have fun, and do what you can. Whatever you can give will be much appreciated.