I am not sure about this specific home since I am a Realtor, not a property manager. However, I do have a 2 bedroom rental in that neighborhood that depending on the pet, might consider it.
Keep in mind that the reason landlords like me own property is because it more expensive to rent than own, so the landlord makes money at your expense. If you are thinking 3+ years in a home and have decent credit (doesn't have to be perfect) there are programs out there that can let you buy a home for less out of pocket than a typical security deposit on a rental too.
Hope that helps!