how can i search for a dog walker without using the on-demand tool?

From a computer or laptop, in the top left corner, you'd click search sitters. Below that for service type, there's a drop down box to choose dog walking, as well as other options. Although it requires a date to check calendar of those shown on results and send messages to potential walkers, you do not actually need to book it at that point (it's recommended to meet a walker first), and there is a second step before it's booked/charged to credit card.