You don't need to be a qatari to sponsor a housemaid. You can either go to one of the agents here (expensive) or get a visa and bring one in yourself. There are some countries which are exempt right now such as Indi; but Sri Lanka, Philipines, Indonesia, Sudan are all acceptable. Go to your embassy, or the embassy of the place you want to hire from, and ask them to give you the details of how to go about doing this.
Many ex-pats bring in their own houseworkers, its fussy and annoying dealing with some of the various offices, but its worth it.

Agencies of course cut out all the hassle, but as many of the girls/men have paid huge bribes I'm against this process and won't use them. If you do hire from an agency, and the worker is unsuitable, they will offer to exchange. Hope this helps.
Angelwings

If the grass is greener on the other side, its sure the water bill is higher !