My vet says to try wet food when this starts. Try one with no grain, like
wellness. It sounds like cat has developed a food intolerance of some kind.
I would, also, get a vet check as vomiting can be caused by so many things,
but at sucha  young age and being right after eating, I'd really wonder
about a food intolerance.

My cat Cheeks barfs regularly, I think because she wolfs
her wet food. There is a particular flavor she just eats faster
than the others. I have begun just putting a bit down and making
her wait for the rest so she cannot wolf. Your cat may be a
wolfer too. Dry food, when wolfed, can make them barf
because it expands. Tony, have kitties had a checkup
lately? It's never a bad idea. You want to rule out any
medical reason for the barfing. (One big reason many
cats do it is because they are eating parts of  houseplants
that can be poisonous. That can be dangerous, so
you might want to look into it.) When I asked my vet
after checking the cats over he said Cheeks probably
barfs because the food is "too rich" for her and she
wolfs it. But I think cats that eat too fast will do it
regardless of the food. The only think I can think of
to do in that case it to ration it out.

Is the cat gorging on the food and then puking?

I had a very similar experience with my cat.

I mentioned the problem to the vet and he said it was normal, even
though I didn't think so. But I went ahead and tried feeding the cat
in small amounts and switching to canned food but nothing helped.
Since the vet said this was all normal, I just believed him since he's
the expert.

A few years later I decided to get a blood test done on the cat (at a
different veterinarian's) and we discovered that he had liver problems
(which was what was causing the vomiting). Unfortunately, by the time
we found this out it was too late. We don't know if he had liver
disease or cancer affecting the liver but whatever it was, it was
overlooked by the first veterinarian. I believe that had he gotten the
blood test when the vomiting first started happening or I had taken
him to another vet, that he would still be alive (and in fairly good
health) today.

I'm sure your cat doesn't have the same problem mine did since yours
is so young but it might be something you want to keep in mind for
future reference.