I understand the sick, sick or not, I'd still keep her. With no fever and moms first week at work it's best to just give her lots of cuddles.
Shes doing the opposite of some kids, some kids scream through their nap on their first few weeks not request one.
I would be inclined to leave her. Since she's sick anyways and could probably use the rest. I have days where I'd just like to curl up in bed and ignore everyone, maybe she's haveing the same kind of day.
I say enjoy it while she does it! Pop in every once in a while, but if she's happy, she's happy.
Maybe try a pack and play on the main floor, maybe she just feels safe in it.