I seem to remember Jennifer Coulter's dog having an issue with a similar type of unexplainable early morning throwing up - can't remember what the outcome was but it may have had to do with adjusting feeding times, as was mentioned. You could try to PM her...
At about 8-12 months old my pup had a SERIOUS case of the morning bile barfies. 5 days a week sometimes between 4-6:30 am. Occasionally before dinner.
The empty stomach thing seemed to play a role. If he went to the door dry heaving, and I fed him (5 am), he would not barf. On the advice of my vet and various raw feeders, I tried feeding him some food right before bed. It seemed to help somewhat, but did not solve it completely. I also tried going to plain chicken for a while, fat removed and added some probiotics, no real change.
I was somewhat worried that he had some pancreas problem or something. Tests revealed nothing. Energy levels and appitite levels always normal.
At the end of my rope (wanting to sleep through the night) I went and saw a well known vet in BC that had been reccomended to me by others from my breed. She is big on raw feeding and homeopathy. I took my dog to her (7 hrs from my town, but on the way from a course we were at). I answered some prelim questions in advance of my appointment. She spent quite a while checking him out and hearing all about him, health, temperment, work. She did more bloodwork to double check a few things. In the end she came up with some homeopathic remedy (which I considered vodoo at the time).
Well, could be a total conink-e-dink, but he stopped having that barfing problem right away. I have never used homeopathy since, but it did open my mind some.
Now he will still very occasionally barf 12-24 hrs after eating something with a harder bone that didn't quite digest (like was previously mentioned in Natalya's post).
He will also sometimes barf bile if he is waiting to be fed at his feeding spot and he is not fed. I no longer feed him extra before bed, just feed normally twice a day. I also feed a huge variety of raw foods now, back when he was barfing a lot, I thought everything form pork to venison to turkey was the culprit. Now he handles them all just fine.
I don't know why he got into that cycle, but once it was broken, life was back to normal. I don't think it is uncommon for dogs to barf bile occasionally, but if it is becoming regular, I would try stop it before it is big deal.
My suggestion would be similar to the advice given to me and to you already on the board.
-See a vet if you become concerned, to rule out other causes(raw freindly prefered).
-Try to keep the diet simple for a while, to quiet diegestion. I would reccomend chicken, low fat and maybe the easily digestable bone parts. (necks, backs) I would almost reccomend ground bone in chicken for a bit. I would at least stay away from turkey drumsticks for a bit. (big bones for your small dog with a bad tummy). If you want to do turkey, try necks perhaps? If you are just feeding necks and backs, remember to add a bit of meat only to get the bone to meat ratio correct.
-try some probiotics (capsuls or plain yougurt)
-when feeding a hard boney meal I sometimes give a bit of slippery elm bark to coat the digestive tract as a preventative. Canned pumkin could work as well maybe.
-I would try adding some tripe, as for some reason I still beleive it can help promote good gut bugs.
-If you get really desperate, try to find a homepathic vet (can't hurt). One with experience, prefrably with references, and one not wanting to sell you a bunch of supplememnts.
I never really discovered the cause, but he has been fine for over a year and a half now. If you are feeding only once a day, you may want to try breaking it into twice, just to rule out the empty stomach thing.
Has the dog been on anitibiotics lately?
Keep me posted, always curious..