Thanks very much for the answers to my questions, they are helpful.
It sounds as if her "vomiting" is a fairly passive process, with not much retching. She may actually be regurgitating.
Regurgitation is a pretty passive process. Whatever they bring up just sort of flows out without much, if any, effort, and the dog just seems to go about their business.
Regurgitation can be secondary to a poorly functioning esophagus. It can be due to poorly functioning esophageal muscles, a weak gastro-esophageal sphincter (the muscular valve between the stomach and esophagus) or a dilated pouch-like esophagus due to a disease called megaesophagus. In some cases this can be due to a hiatal hernia as well or a condition where the stomach everts itself up into the esophagus. In Some snub nosed breeds rather then a straight tube the esophagus has bends and pouches where liquids can get caught. Some of these dogs will outgrow this, they grow into their esophagus.
I would discuss her symptoms with her veterinarian. We can evaluate her esophagus with a simple test called a barium swallow. This test involves giving her barium to swallow and then taking a series of radiographs to evaluate it's shape and function.
Treatment will depend upon what is diagnosed and can be as simple as giving her time to grow, acid reducers, medications to improve esophageal function, or changing the consistency of her food or surgery.
In the meantime continue adding a little water to her food, giving her very small amounts of water at a time or trying ice cubes so she cannot drink too much. It may help as well to keep her upright (front feet up on a bench) after she drinks for a good 10 to 20 minutes.
You can also try acid reducers which will help if this is related to gastroesophageal reflux
1) Pepcid ac (famotidine) at ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours
Best of luck with your girl, let me know if you have any further questions.