Hi Abbas,
you may find for around 1000 USD to 2000 USD, but probably with more rooms than 2 or 3. Because if it is a house usually the houses here are bigger with 3 or 5 bedrooms, and the garden you have mentioned. Actually depends of what you are looking for, if you want to live in a complex with electricity might be a bit more expensive. And if there is furniture it is more expensive. If you want an apartment you may find with 2 bedrooms but without the garden, and should be cheaper, without the furniture my friends rented for 650 USD, the apartment. There is a group on facebook called Buy and Sell Erbil and you can also see some houses to rent or even post asking for a house in that condition. For what I have seen it's a little bit easier to find without the furniture. That's my opinion.