Sorry to be specific, but you don't say whether she needs a pee or a poo (or both).
Roly had a similar problem (needing a poo in the very early hours), but I traced it to his food. It was a good quality food (Burns), but it just made him need the loo quite a lot. As soon as I changed his food he was fine within a few days, no more early morning calls. Also at last bedtime toilet, he had to do both a wee and a poo before he could go to bed (however long it took) - he soon got the idea, and now its habit.
At the time he was sleeping downstairs and was under a year old - I was also getting up to let him out, and the one time I didn't he did a poo in his crate (the only time ever), so I felt very guilty because he did ask (howl) to out.
If she is needing a pee, you could try restricting her water after say, 7pm at night and feed her a bit earlier (mine are fed at about 4pm).
Just a matter of trying a few things along with a review of the housetraining - hopefully you will find a solution.