Re-home the cat? I'd rather re-home the child!(only joking)
Seriously though,you can sort this without extreme measures,but maybe threatening your daughter with that might actually help.I'm sure she doesn't really hate the cat,she is just picking on it. Sometimes kids go through agressive phases.If she were hurting a younger sibling you would stop it swiftly,just because it's a cat you shouldn't have to think of removing it,even temporarily.
Be firm,consistent and show her how cross you are about her behaviour.I don't care if she's tired,jealous,or whatever,make sure it doesn't happen again..or else!
Let us know what you decide to do and if it has worked.