@elanpro43 I mention merely out of interest, here in the Middle East where I live, every single pet store in my city offers free same day delivery. It is a competitive business. From what I can tell, it is sometimes the store owner who handles the delivery in the early evening when he closes the store, or it is an independent delivery guy with a bike who handles deliveries for a few stores.
Because it's assumed the customer and store are in the same neighborhood or close enough, the travel costs are very low.
This means that this is testable. Talk to a few pet stores within a neighborhood and see if you can do deliveries for their customers for a month. It will highlight whether it is feasible or not. The good news is that once a customer expects free delivery, everyone will have to offer it.
Also, worth noting, I sometimes order pet supplies from a store outside my city. Now, when they know they have a delivery in my neighborhood, they call me to see if I need anything.