I really feel for you. My DD was exactly the same. I spent the first 18 months chronically sleep-deprived, especially as I went back to work when she was 10 months and DP hasn't once got up in the night. We went through a long time of 4:30 and 5:30 starts.
Now DD is 2.6. She always wakes up early, no matter what time she goes to bed, at the moment its 7am (but we're in Germany for a few months, so thats 6am UK).
There were no magic cures for us I'm afraid, I just went to bed at 9.30 for a year and a half. None of the other mums understood why I was finding it all so exhausting!!
The things I did, which may or may not have helped were:
Not feeding her as soon as she woke up in the morning (once I was sure that it wasn't hunger waking her up) to stop her waking up for an early breakfast out of habit.
Giving a dream feed at 10 or 11pm (can't remember though how old she was when I was still doing this).
Keeping the room extra super really dark and following the same routine religiously.
Being careful about room temperature and using a grobag to make sure she stayed at the right temperature overnight.
Not rushing in as soon as I heard her first peep in the morning, to see if she would either go back to sleep (yeah, fat chance!) or amuse herself for 10 minutes.
Now as a toddler I find the more secure she is the better - nice dark room, familiar things, cosy, small bed.
I really hope she starts sleeping a bit for you. Good Luck!