I would immediately check to see that it's not ascites. (If it is, you can aspirate it using a syringe. There are some good videos on youtube.) Basically, there are various causes, but the symptoms are a buildup of fluid in the belly which will eventually squeeze her internal organs if not removed.
She could also be egg-bound. Has she pooped? Can you get a picture of any poop or do you not recall the last time she has pooped? Badly egg-bound birds cannot poop.
Another possible cause is fatty liver or obesity, which you can't really treat except with dieting.
All of these are serious conditions, and her being "low and round" makes me think that she has one of them which must be treated immediately.
I agree if she was full of eggs she most likely wouldn't be here any longer, but if she is acting fine eating and drinking, pooping then like chickens really said she is most likely taking a break. My Muscovies will lay for a few weeks then take a break.