Of course. You can create a special price for the dog owner in 2 ways:
If you received an Enquiry from the owner, when you click "pre-approve" you then have an option to "edit" the price.
If you already have a relationship with an owner, you can create a Custom Booking for them. This means you start the booking process instead of them, so they simply get a notification to confirm and pay. It's super easy: go to your Bookings and Messages and "Create a custom booking". You will have to select a contact (dog owner) and indicate the price, service and dates.
Note that if you receive a Direct Booking from a dog owner, because payment has already been authorised, you cannot edit the price. In order to offer a different price you would need to decline that direct booking and create a (brand new) custom booking so that the owner gets notified and confirms/pays.