Is it safe to deep clean my quail cage with a broody Quail in it?

[Oob Child]

I have a broody quail and I really want to deep clean the cage without disturbing her broodiness. I wouldn't remove the nest or properly scrub stuff, I would just remove the bedding and swap it as well as wiping down the fake plants.
Can I do this without stopping her from being broody? How should I go about it? I was planning on doing it but then she started to show signs of being broody and I didn't want to disturb her. The cage really needs cleaning!

Here's the nest, there's about 14 eggs in it now.

 

[Nabiki]

You really need to remove some eggs from that nest. There are too many there for her to hatch, and if the ones in the middle keep getting pushed to the edges, none of them will hatch. If she's seriously broody, she will go back to the nest after you clean and take some of those eggs away.

 

[Oob Child]

You really need to remove some eggs from that nest. There are too many there for her to hatch, and if the ones in the middle keep getting pushed to the edges, none of them will hatch. If she's seriously broody, she will go back to the nest after you clean and take some of those eggs away.

I did clean the cage and took away 10 eggs, marking the others. She had 16 eggs.