Thank you for your question about Snowball.
Vomitng in the morning could mean that her insulin dose is off. It could also be due to her stomach being empty, or to any of a dozen other reasons. Cats vomit for so many reasons that it can be hard to tell.
If she only vomits in the morning, it it before she gets her insulin? If so, it is probably not due to too much insulin. If it has been 10 or 12 hours after her last dose, the insulin has probably peaked before then. But the only way to know would be to do a blood glucose reading at the time she vomits. If it is really low, she may not be getting enough insulin.