Lots of good suggestions here. I know it is temping to try to price things out. But in service businesses like pet or farm sitting is really going to depend on what sorts of pets and how many you are caring for. Do pick a “minimum” charge for one visit a day - regardless of how many pets. Say your minimum charge is $10 - so you might say on your web site or wherever you advertise, “price is determined by number of visits per day and number of animals cared for, with a daily minimum of $10”. That way folks know the absolute minimum cost, and you will avoid getting requests to come feed their entire menagerie for nothing.
You should also pick a range of miles from your home base that you are willing to travel. Like “My service area includes 35 miles from Applejack city. Additional fee applies to clients that are beyond that.” or “quoted price includes 45 minutes travel time one-way - addition fee applies for every 15 additional minutes”. Or something like that. After all, you wouldn’t want someone to call from three counties away and expect to pay $10 a day to come feed their one cat.
Figure out the average gas mileage of your vehicle, then using current gas prices, figure what it costs per mile. Then figure it out based on gas being 50 cents more expensive per gallon. Then average the two. Whatever that cost is needs to be built into your minimum price structure. Because you’ve at minimum got to recuperate your gas money. Using my lovely 20 yr old Suburban that gets 13 miles to the gallon max (on the interstate!) as an example - if I serviced a 25 mile radius, then at $10 minimum, I’d not break even for that 25 mile trip one way, because the gas alone would cost me $10 to drive 50 miles. Hopefully, you aren’t driving a 20 year old Suburban!
Get some jobs now pet sitting before you launch. Do it for free (or perhaps just for gas money). Then have them write you a reference that you can put on your website. Or if you have already pet sitted (sat?) for friends or family, have them write you a reference.
I would also recommend contacting your future competition and getting price quotes. Pretend you are going out of town and are looking at pet sitting options, vs keeping your pets at a kennel. Good way to find out exactly what others charge.
I had a pet sitter last November to take care of feeding, putting out hay and picking poop in my 2 run-in sheds and just making sure everyone was OK for our three horses (once a day). My mother stayed at our house and took care of our cats and dogs, and fed the horses in the AM. The sitter came in the PM. She charged $25 a day, which I didn’t feel was enough. So I tipped her $100 on top of her fee (our vacation was 10 days, so basically $10 day).
Good luck with your venture! 