I should make it clear I'm no expert on this - only a few months into chicken keeping myself. I've got a broody at the moment and it all started exactly how you described which is why I replied - she also started lining the nest box with feathers. I didn't really want her to be broody so I kicked her out of the nest box (not literally, you understand) whenever I saw her. The first couple of times that seemed enough for the day but then she was back in there the next morning. Then I tried putting her in a run by herself with no access to inside space and she just brooded in the corner. I was just about to go to the stage of constructing something from pallets so that she had air underneath her too when I just thought it might be easier to let her sit (I have hopefully fertile duck eggs). She's been sitting a week now and seems thoroughly dedicated to it.
The ideal anti-broody pen which is something with a wire base too so that they get a breeze through their underparts and it's not comfortable to sit. Something like a bird cage. I believe it takes a couple of days in there. If you Google, you should find some images. There was a make your own one in one of the smallholding magazines a few months back but I'm not that handy (hence my makeshift attempt with pallets).
Personally I'd start with just moving her on and seeing whether she's serious enough to need to move it up a level. Alternatively if she seems really serious, you could order some hatching eggs in and have yourself some cute little chickies in a few weeks, followed by tasty dinners in a few months,
H