She's too young for cc (agree with Twiglett about six months being the youngest you should try it) and I personally wouldn't call a 5am wake a night waking. I'd call it a disgustingly early morning waking, which small children are distressingly prone to . I'd probably suggest trying to get her back to sleep by any means possible, or get up with her, then when she goes back to sleep a hour or two later, jump back into bed yourself for a bit of catch-up kip. It will probably be better once you are at home.