You can certainly call a real estate office there and ask for their rental dept. It's generally not worth it for more modestly priced properties to list with real estate agencies, and the big developments all do their own marketing, so rental agents would mostly have higher-end single-family homes or smaller multi-units. You may also need to pay broker fees (sometimes up front) for looking that way. Not to discourage you to try that! If you have very specific needs, a local rental agent may be well positioned to help you meet them. Pets will likely be a big issue when renting, though cats may be easier than dogs. Coldwell Banker has an Airport Regional office: (412) 264-8300
Given this rental price range, have you considered buying instead? Whether that makes sense depends of course on your future plans, willingness to take on the responsibilities of home ownership, and other factors, but given interest rates under 5%, it's likely attractive financially. Your mortgage payment could be comparable to your rent payment, and you wouldn't have to worry about pets. It's a big step, and home ownership isn't for everyone... just something to think about as you search. Good luck!
Some apartments to consider:
2BR duplex in Coraopolis $550 w/pets: http://pittsburgh.craigslist.org/apa/2430523127.html
2BR triplex in Coraopolis $750: http://pittsburgh.craigslist.org/apa/2445797098.html
If you're looking for more amentities, there is a 2BR in Carnegie for $949: http://pittsburgh.craigslist.org/apa/2454157403.html
Hope this information helps. Please contact me if I can help you further in your search.