When we brought our kittens home they were 11 weeks old. We set up a single room for them with everything in it (for them, this was essential as they didn't want to leave it for a couple of weeks - being in a new space can be incredibly daunting for kittens). Make sure there are safe hiding places and put the bed somewhere that feels sheltered. Put as much space as you can between litter tray and food, and don't put the food next to the water. Don't be surprised if it takes her a while to settle, even if she's been a confident kitten before.
Make sure the room is safe for kittens, e.g. put cable protector on any wires, check there aren't aren't small things lying around that she might try to swallow, remove any breakable ornaments, if there are any plants, check they are not toxic to cats. If there are any hiding places that could cause issues in terms of her getting into a space she could get trapped in (e.g. a chimney breast with a gap in it, or a loose plinth under a cupboard), make sure it's blocked up.
Take it very slowly re introducing the dog.
The advice I was given was to open the carrier when they arrived, and leave them to come out by themselves, but if they didn't, after half an hour, take them out and show them their litter tray, food and water. Ours just sat in the carrier so after half an hour I took them out and put them in the litter tray. They then started exploring the room a bit by themselves and found themselves a space space on the bookshelf, but they knew where the litter was and we had no issues with them using it. Make sure you start with the same litter as she is currently on, to avoid any confusion (you can change later if it's not one you like). Also stick to the same food at first.
I don't know if a cat tree is essential immediately, but I'd say do get a scratching post. If it's possible, create an area where she can climb onto as being high can make them feel secure. But if you plan to get a cat tree anyway, no harm getting one now.
Toys: cats are all different so you could get a bundle and see what she likes.
As she is coming by herself, you may want a heat pad in the bed as she will be used to curling up with mum and the rest of her litter. You'll also need to be around for her a lot as she won't have a companion to play with or keep her company.