Before finishing my profile and paying for the background check is there a way to know if there are dog walking jobs available in my area?
Nope, because that is not the way Rover has chosen to operate. When owners post "Help Wanted" type ads, they're gong to be inundated with responses from sitters or walkers. While it may be more work for owners to read sitters' profiles and contact several before meeting and making a decision, it is ultimately better for the customer not to be barraged by zillions of responses, many of which may not even be suitable.
There are or were other sites that operate as you described. But I do understand why Rover has elected not to go that route.
I think he means whether or not rover is actually in his city yet or not. Not whether or not there are actually jobs available. I agree with your sentiment, just think you missed ops point.