Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your little one has eaten poorly, and vomited 3 times this morning, with the one of the vomiting episodes containing an insect.
It is entirely possible that her vomiting was triggered by eating the insect. Some insects are toxic, but most simply secrete a horrible tasting substance as a protective measure. This protects them from being eaten in most cases, but if it doesn't that can lead to nausea and vomiting.
If the insect were truly toxic I would have expected her to continue vomiting. I am pleased to hear that her vomiting has stopped and she is able to sleep.
The good news is that the bug is out now. She should feel better when she wakes.
If she doesn't feel better then it is possible that something else is making her feel poorly.
She may have a bacterial or viral infection or she may have eaten something else that you are unaware of.
If she is still feeling poorly when she wakes there are things that we can do to settle her stomach, but if she isn't responding quickly then a veterinary visit is in order as she is still a baby and doesn't have many reserves.
To try and settle her stomach today and improve her appetite you can give either:
1) Pepcid-ac (famotidine) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours.
These will reduce stomach acid and should help if this is related to simple nausea and gastrointestinal irritation.
I would wait to feed him any food
for 2-3 hours after the acid reducers are started. This should help stop gut spasms and restore normal gut motility. Small amounts of water or clear broths like low salt chicken broth or tuna juice offered frequently are fine as she needs fluids. You can give her pedialyte to replace electrolytes too, though most cats don't like the taste.
Then in a couple hours if there isn't any vomiting offer her a bland diet mix of 2/3 boiled, white skinless chicken, all fats and juices drained off the meat, mixed with 1/3 boiled, plain white rice. Feed several small meals a day.
Once she feels better (no vomiting for 48 hours) start mixing in her regular cat food very slowly, less bland more regular with each day. It should take a week or so to convert her back.
If she is continuing to vomit, runs a fever or has a tense painful abdomen and is feeling poorly though it would be best that she see a veterinarian now as anything you give her orally will just come back up worsening her dehydration.
Best of luck with your little one, please let me know if you have any further questions.