I’ve never personally dealt with the regurgitation for being sick (thank god) or mating (I see it coming in body language and I quickly divert his attention). I would definitely take the advice from the others above and see a vet. It could be mating, as every bird is different, I would just find it a tad unusual given you have not had her there long she’s doing this out of mating behavior. This being because of what JLcribber said, you’re well at the beginning of where they’re still scared and haven’t let their guard down. Which leads me to believe maybe it’s something for a Vet to check out. In the mean time, consider things such as diet changes since she’s lived with you, sleep schedule changes, etc. Moving is stressful, especially for cockatoos who tend to bond strongly to their owners. And She could have picked something up during the relocating.
Given its unusual behavior for a female if it’s mating, are you sure it’s a female? Has she laid an egg for the previous owner or been DNA tested? She could be a He. And it is that time of year. I happened to walk in on a “session” my cockatoo was having with a toy in his cage when I came home from work the other day......I have since moved the toy so he couldn’t lay it on his neck (that’s his thing for some reason).