If a kitten is throwing up and has diarrhoea, it is definitely worth a trip to the vet just to be sure. Kittens are so tiny that they can dehydrate quickly, and if this is a worry, the vet can put your kitten on a drip.
If it was an older cat I would say wait at least 12 hours unless the cat was showing other symptoms, because cats often eat something that doesn't agree with them, get fur-balls, eat too quickly or too much (my youngest cat is always doing that) and it's not something to be too concerned about.
In this case you would take away all food and water and keep a close eye on him/her. You could give her water in tiny amounts but no food at all until the next day. If the diarrhoea has stopped by then, try her on bland food such as a little chicken mixed with boiled rice.
Why your kitten might be throwing up
To be honest, even with my older cats, if they had diarrhoea and vomiting at the same time I would take them to see a vet. Your kitten is young; I wouldn't wait. It's best to be safe and even if the vet just checks her and says all is well (fingers crossed) it will be worth it for your peace of mind.
I hope all goes well and that your kitten is his/her usual bouncy self very soon.