A girl dumped you and then asked you back out is that a sign of desperation?

Depends if she tried finding another guy or not and was denied, then came back to you. Then yes.

or she might think she can't get anyone else so she asked you back out, but there is no way of finding that out.

or she coulda just needed a break to think things through.

I think its a sign that the girl is a jerk.