Our 5 month old puppy is at the vet right now for a similar reason. After taking an x-Ray of his abdomen it appears that he has eaten a few of the kids toys. He is probably going to have surgery.... My understanding is that "vomiting" can come from a wide range of reasons. I am curious as to what did your vet do (x-ray etc..) before recommending going to a specialist?
Hope you'll get this issue resolve and that your pup feels better soon.
F