Its hard to speak for availability this early, but you should begin the search a month or two out.
Are you looking for a house, condo, or apartment? Also, what size/ type of pets are they?
A two month lease is not typical, so a better route to go may be Craigslist, since you can bargain with the landlord about a two month lease. Use at your own risk, and be careful on Craigslist, it can be pretty shady.