I think if she's giving you the dialogue about 'there's no plot of land for sale' instead of 'Tom Nook said the island is full' that means you have a missing housing plot. If you have all 10 villagers, maybe someone is in boxes? or someone moved out and the empty plot is already reserved? Or maybe you (or another player) started to move someone's home but never placed it and the building kit is still in inventory somewhere? You can only have one villager/home in the moving process at a time, so I don't think a camper will move in if that's happening.

I'd probably check on all 10 houses and make sure.

(But also they always refuse a bunch of times before they agree to move in, so if it's none of those things, maybe just keep talking to her?)