I am not going away until March, Do I have to pay now?

If you click book it now, then yes your credit card will be charged -- Rover holds onto the funds until after the stay is complete. To avoid paying in advance, I'd suggest when you & your pet meet with the sitters of interest (I'd suggest a backup or two in case availability changes), ask if they can fit you in those dates and book it when it gets closer to that time.