Kind of interesting question. My kids have gone to swimming parties, but I didn't buy them a pool. They've gone to laser tag parties, but I didn't buy them laser guns. Bowling, but they don't own bowling shoes. Or balls. We've gone to all kinds of parties that didn't result in $100 investments.
You don't mention how old your child is, but if she is school age, I would handle it this way:
1) I would explain your position on the party and buying the doll.
2) I would explain that she doesn't take care of her toys now as it is.
3) I would take her to the party to celebrate her friend's birthday (seems kind of selfish not to go just because of that - it's the kid's birthday and she wants friends to celebrate with!), and I would let her play with the doll. Then, I would offer that if she really, really wants the doll, she will have to earn it a) by taking care of her toys now, b) by choosing some things to sell now to declutter and make room for a new toy, c) by doing chores to show responsibility. If she wants something badly enough, this would be a good teaching experience for her. And honestly, you'd be teaching her that jealousy trumps friendships by not taking her just because she wants the doll you won't get her.