Gosh! Dogs are all so different aren't they?
I had a dog once who used to love raw carrots, I'd give him one instead of a dog-chew treat They never upset his tummy.
My other dog (the one I had recently, though she passed away last year at 15) couldn't tolerate raw carrots. Either she threw up after eating them raw, or completely ignored them. But if they were cooked, and added to her food, in small amounts, there was no problem. She was always a very healthy dog, but just couldn't handle raw carrots!
Maybe yours is like that...?
It may be best to try her with cooked vegetables, and make them a small part of her meal, not a large part.
Yes it was raw. She threw up again actually this evening & it still had carrot bits in it. The second episode could have been because her stomach had been empty for so long, she throws up bile if she goes too long between meals. But it could also still have been the carrot irritating her or it could have been both.
At first she didn't even know what to do w/ it, she was licking it for awhile then tried several times to pick it up, then would drop it, she's a Shih Tzu so she's got that short snout. But eventually she got one in her mouth and figured out to chew it up and seemed to really enjoy the other three pieces. Oh well, I guess she's just not going to be able to eat anything else. I've also got canned pumpkin here at home, was hoping I could use that if she ever had a bought of diarrhea again, but now I'm afraid to. Also the Vet gave me some Composure chews for her to help w/ anxiety/stress the next time she goes to the groomers (which is what set off the last bought of diarrhea) and now I'm afraid to try her on those too!
My experience with dogs and carrots is some like them some don't. I have never observed any regurgitation by those that would eat raw carrots. You didn't say raw, but I assume that is the case.