Settling in my first ever kitten

Hello! I'm hoping someone could offer a bit of advice. I'm a little overwhelmed at the moment...

Last week, we discovered that a 8-9 week old kitten was living under our shed. On Sunday morning we trapped it, gave her a bath, and tried to get her settled into a carrier. Well, she didn't like the carrier--she'll tolerate it only for a few hours at a time before making a fuss. So, this morning (after I was woken up at 5AM from mewling ), we let her loose in my bedroom with the door shut. Later that day was the vet appointment, where we discovered she was mostly healthy except for roundworms. In 30 days, the vet will do more tests for diseases like leukemia.

This kitty is very friendly, but a little skittish. I suppose any animal would be in a new environment. To demonstrate how good she is, at the moment she's curled up next to me in bed! She'll also play with some toys and let me pet her while she's eating. She has a tendacy to hide under my bed/dresser, but I'm hoping that for now it's just a comfort zone.

My questions are thus: How do I know when it's time to let her explore the whole house? And how do I go about that? Our house is very small (but also very open) and has a LOT of hiding places. It's easy to say to kitten-proof the house, but there's no real easy way to go about that when there's so many spots she can go into. I'm also concerned about the basement; there's no door to close it off and we own no gate. Should I invest in one or am I worrying too much?

If you are home with her most of the time, I'd let her roam the house under supervision. I would make sure she knows where her food/water are and her litter box. And don't put them right next to each other.

As long as you can get her if she gets stuck under the sofa, and you can tell where she is, she will be fine!

Congratulations on your new addition and welcome to the wonderful world of being owned by a cat!

Congratulations on your new kitten!! You're in for some really fun times!

If you have other cats, do not let the new one get near the little one since she's not been tested for any of the kitty diseases. If you don't have other kitties, then there's no worries. Since she's so tiny, I would recommend leaving her in one room w/ food, water, toys, litter box, until she is used to your voice, her name, your touch, and the sounds of your home. Then in another week or two, let her explore more of your home, but at night, bring her back into "her" room. Once she's more comfortable with the larger area, give her free run, but provide lots of safe places and litter boxes!