Remember to keep your kitty's nails trimmed! The only time I ever feel little pricks from her claws is when they've grown long & sharp enough to start curving longer than her sheath when retracted. I've trimmed my cat's nails since I got her at about 10 weeks. While she was still at the kitten stage, before she mastered the art of jumping and quit the habit of "climbing", we got a lot of destroyed leather furniture from claw tears. After a short period of discouraging her habit of climbing her daddy's leg like a tree, that stopped too, and saved his legs and pants! He thought it was cute though it started hurting him with the pricks LOL. Also with a scratching post/condo and/or carpetted door mat as we used that early on
, my cat never scratches anything else. At the very beginning, when she'd scratch the carpeted floors and VERY early on, the door frame(s) (remember to not let them start a habit of climbing door frames even if you think they'll "grow out of it" like my brother figured with his kitten
), I'd take her straight to where she SHOULD be scratching and holding her paws gently up to it and making the paw/scratching motion with it while telling her, "Scratch here~ Good girl!" and she picked up after a few corrections and has lasted her lifetime thus far even after relocating.
She'll be 9 this spring. I'm proud to say I've raised her to be a gentle kitty who plays by "kissing" (that's all mommy ever does with her, hugs & kisses) except when she's kicking her favourite ball around or tossing her little plush toys with her mouth into the air. She "bullied" my old shihtzu into giving up the best tanning spots by the glass door with the best view, etc, by "grooming" her relentlessly. My old dog would just get up and move to another sun spot to tan and nap in peace. They never played "chase" as all they did was either curl up together to sleep or my shihtzu would permit the cat to groom her. Our cat put up with our shihtzu's 3-hump greeting everytime she comes back from somewhere and grabs a hold of her to say "hi".
I had a fairly laid back adult dog before the kitten and so she's never really had anyone to play "rough" with as she's been raised as an indoor-only cat. Now, it's as rough as she's capable of responding to my yorkie's "play". When my yorkie isn't chasing her, minding her own business, chewing on a bone, etc, she'd dash pass her repeatedly to taunt her so we know she WANTS to be chased... actually, what it's becoming is, our cat LOVES the recently started bum-licking service!
It all started in the past two weeks or so while I did my usual snuggle & kisses with Pichu and smelled kitty #1 & #2 on her facial hair! I know she doesn't get to the litterbox as I'm with her always and the house is fairly quiet, and she's been taught not to enter the room where the litterbox is placed and if she does, she's usually caught long before she can reach the corner where the enclosed litterbox is (has a swinging door/lid). So I know she doesn't get to eat kitty droppings. She doesn't even eat her own. Later I witnessed her giving my cat generously LONG licks on her bottoms! And my cat leaves her tail up to make it easier access!! This is their new game! Previously, it was just annoying the cat with a series of play bites on the ear/scruff (behaviour she learned from the cat when the cat would nip her lightly ONCE on the ear to stop her relentless wrestling and play nipping). The cat also "bops" her on the head/face to stop the hyper jumping/pouncing, but never with claws out. There are times when she'd let out a yelp but jumps right back into playing. I've witnessed it multiple times before and so I don't get worried over it as it's sometimes just a yelp in anticipation of a "nip" but she's more aggressive than the cat ever was, so it's all good... though now my cat's quite a bit overweight, she can just "sit" on her and stop her if she felt so inclined, but never have used her weight to her advantage even when they're both on their hinds to out-height the other.
So anyway, I don't think it's a problem introducing a kitten to a dog/pup or other animal household. They get used to it young and learn to be the best of friends and would more than likely play at your dog's level... and I would think it'd learn to be friendly with your rabbits too. I might go with a female cat over a male one just in case. Though male cats are very very affectionate, they may put up with less in terms of dominance or hyper behaviour, etc, but not sure about males at a young age.