Try raising her dish about 4" off the floor so she is eating with her head level with her shoulder blades.
We call this "scarf n' barf". Usually it's just caused by nerves. Your cat could be nervous about the one dog and scarfing her food because she's afraid he'll take her food from her.
She may also have a touch of megaesophagus. This is when the esophagus dilates and the muscles don't quite coordinate properly to move food along.
As a result, food backs up in the esophagus, and when it gets full, up the food comes.
Because the esophagus takes a sharp bend where it passes the heart, food often backs up at that point.
Forcing the cat to eat with her head/neck stretched out straight will straighten out that bend, force her to slow down, and might very well stop a lot of the vomiting.
If this is something that started recently, take her to the vet to rule out other, possibly dangerous conditions, and to get her teeth checked to make sure she isn't chewing her food properly due to pain in her mouth. At 6 years of age, if she hasn't had a dental yet, her teeth may very well need some attention.
