How old is your baby? and how big?
Ziggy did this a few times and his was caused by hunger, he would sleep through the night and wake up too hungry and... well then the bile would come up. i asked my vet and he said its hunger due to his tiny size () he is around 3lbs now so at that time he must have been about 2.5ish)
If you're going to your vet anyway, i would bring it up and see what he says, you never know and i trust my vet so I asked (I called and asked and he said i didnt need to come in and explained it to me)
He hasnt done it in so long, now i make sure he eats right befor we go to bed and he's fine.
Hope its nothing serious with your puppy. Let us know how things go with her