I agree with Wilda. www.vrbo.com is a great website, and you can filter for pet-friendly properties.
Please be very careful though, there are scammers that will "scrape" the information off a real ad and re-post at a lesser price. Then they disappear with your deposit money.
Dealing with a reputable property management company might be worth considering. I've heard great things about www.NWTucsonRentals.com and Apartment Locators, as Spirit mentioned below.
Enjoy your stay in Oro Valley!
Long Realty Company
10445 N Oracle Road #121
Oro Valley, AZ 85737