She needs to be in DC now to start putting together a staff, unless she thinks she can just round up a crowd at Starbucks.
Yes. But she will still have an apartment in her district, so now she needs to pay for two locations; and while she probably has enough money to do that, there is no requirement to have money for travel and lodging and daily expenses, even though the job clearly needs you to be in DC, before you actually start getting paid.
So you have a job, it requires you relocate and start “doing the job”, like training and hiring, but you have no money to do so until January 3rd. They should probably fix that. You should in fact be able to pay staff people maybe a month before you become sworn in, because you need to be able to work from day one.
I don’t think that would be unreasonable, to provide a per diem and a staff allocation starting December 1st, for new members.