If and owner wants a 4month contract, how do I get paid weekly?

The only way to be paid weekly is to do weekly bookings. Explain to the client that if they do a 4-month booking they will be charged up front for the entire amount and they will probably rethink the entire booking. Using your walk rate of $18 here is an example: 5 walks per week M-F x 16 weeks x $18 = $1440 plus Rover fees on top. Best of luck

Create a booking for each week.