I'm afraid that your price range is a bit on the low side. In this very active market, with inventory at or near an all-time low, you're looking at at least $1500 for a single-family home in a more desirable area, most likely more. You'll also be paying a pet deposit, which could be substantial, depending on the size of the animal. Hopefully, it's not a dog noted for aggressiveness, in which case you'd have an incredibly difficult time finding any sort of housing.
With families unable to find suitable homes to purchase, many are leasing, which has depleted the number of rental properties available. As a result, prices have risen considerably, and continue to inch upward.
I wish the news were better. Best of luck.