Hi,
I would say she is overtired at the moment which will probably be causing the early waking, and habit is probably the reason for the night waking. I am no expert, and aren't sure of the amount of sleep a 13 month old should be having, but would think at that age she should maybe be having a nap and a short catnap to prevent overtiredness by bedtime (I'm sure someone will reply to this soon and let you know for sure).
I guess the next step would be to work on getting your dd to take a morning nap, if she wakes at 5am what time do you try and get her to nap? Maybe she is overtired by that point so you should try earlier the next day. How does she go to sleep? Do you have to rock her or does she go to sleep on her own etc. Not sure how much you know of BW, but maybe read up on the sleep techniques and prepare yourself for walk in/walk out or gradual withdrawal if you think she might need to learn to go to sleep on her own (especially to wean her off the nightfeed).
I'm not sure how many changes you should make at once (again, sure someone will come on and let you know). I'm not sure if it would be too much to attempt day naps and weaning from nightfeeds at the same time, would be tough on you both, but maybe you feel you are ready to tackle everything at once?
Keep us posted
Sal
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