Take a look at
"Dawn Phenomenon", see the tag below or use this
link if you need more information. It can be very discouraging.
If you are up several times during the night with the young one, I am sure that this could play a part. Several people have found that eating a small snack before bed helps. I see that you are currently doing this. I have found that a hand full of almonds works for me. Good luck in your search.