Kittens are energetic bundles of fur and mischief, and that's as it should be, but it can some as a shock when you've never had a cat before.
However, even if you've been used to dogs and havent ever had a cat or a kitten before, one distinguishing feature between them (and I love both) is that an unruly puppy seldom grows into a calm dog without owner intervention, whereas kittens, as they mature, generally adopt a more reserved demeanour.
I say "generally" because of course as Gill pointed out, all cats are different, and for sure they react very differently to dogs. It's a delicate process "teaching" a cat, and you cant apply dog training principles, cos they dont work. Punishing cats especially doesnt work.
If you dont want her to interrupt at mealtimes, you could try giving her alittle bowl of food of her own when you sit down to eat. however, if it's more about the interaction with her humans than it is about the food, she'll continue to want to be with you whilst you're eating - it's a very sociable thing for a kitten. If that's the case, you can just gently pick her up, place her on the floor and say "No" firmly. You'll need to keep doing this, and if necessary to ignore her when she repeats her efforts to engage with you.
Just a personal thing, but I love any engagement with my babies, because it means they want to hang out with us, and it's helping to forge the bonds that will take you all into hopefully a long, happy adulthood.
Sadly, many people lose interest in cats once they become adults, because they think the cat has lost it's "fun" element. but that does a cat a huge injustice, because as everyone who's ever really taken time to understand their cats will tell you, the inner kitten remains with the cat well into old age.
There are few things more enchanting than witnessing a cat having a play session when they think no-one's watching - or when they know you're watching and they don't mind or care.
The key is to study a cat's body language and learn how that works, in the same way you would come to instinctively know how to interpret your dog's "language."
Don't be put off having chosen a kitten if it now turns out you feel a bit unprepared.
You'll learn fast, and as you've no doubt found out by now, we're all happy to chip in with advice as and when you need it.
It's great she's getting on with your dogs too.
We combined cats and dogs happily for many years, with one of our cats acting as the eyes and ears for a dog we had who went blind and deaf in her later years. He went everywhere with her, and was very protective of her.
Got any more piccies?