Yes, you may be able to save something.
You should be able to get a two-bedroom unfurnished apartment within QR.5000. Your monthly household expenses will be around QR.2500. Add another QR.1000 for miscellaneous expenses. The rest should be in your pocket.
You will be able to find maid servants for daytime work but they are going to be costly. As for you finding a job in Qatar, try your luck out. The competition is tough.