I didn't reply to this as I thought C.C's Mom hit the nail on the head.

If the problem persists past six - seven months then some other strategies may be useful but there is every chance she will grow out of it.

A couple of things to think about in the mean time - does your heating system or hot water tank fire up at this time? It could be she hears that or is too close to a heat source that switches on in the night? You could try resetting your timers or moving her crate and seeing if that makes a difference.