I am an adult signing up to sit http://rover.com dogs, can I have my 14 year old daughter sit the dogs for me?
According to Rover Terms of Service, my understanding is no. Note the Terms of Service sections 2.3.1 - Compliance w/Laws (must be able to legally work) and 5 - Age Restrictions on Use of the Site or Services. Since it is a written contract, no person under 18 could enter. Yet, in my area, I've seen people stating it's an adult or two and their minor child/children providing service. Perhaps you want to contact rover support directly.
Personally, I would be highly uncomfortable if my dogs were to be left with a fourteen year old. Because they are a minor, in the case of emergencies, they would most likely not be able to provide proper assistance. I do believe you must be 18 to have a Rover profile at all so if you create one merely to advertise your daughter's services then you are deceiving potential customers and violating Rover.com's terms.