I really don't see the appeal of Hawkgirl. Her origin is interesting in the context of her relationship with Hawkman (to be fair, it works the other way around too in my opinion), but as a standalone character, not so much.
Does she have any powers other than her wings and N-th metal mace swinging ability? I know powers aren't EVERYTHING for a hero/heroine, but since she doesn't have much else going for her, I don't see how she'd make a meaningful contribution to the new movie universe besides the idea of having the ever-so-loved DCAU lineup.
If this team gets another female character, my vote would be for Zatanna. Since she's likely going to be in JL Dark if that ever gets off the ground, this doesn't seem likely. So a second choice could be someone like Black Canary. Seems kind of contrived, but she's got enough backstory to warrant her having a sizable role.
If they're feeling adventurous, they could use Element Woman? That may require Metamorpho first though.