Hi Lynn,
I recently arrived here and went through all those questions. As far as your visa is concerned it will take between 4 to 8 weeks to process, depending if you're sponsored by your job or by your husband (much longer). Until you have your own visa you will not be able to sponsor your maid. Although the final sponsor will be your husband, he needs to be married & prove his wife is a resident in Qatar before applying for a visa.
You already have the maid, and this is a wise idea to take her with you, cause things here are a bit messy. A lot of people without visas or working illegally under a Qatary sposorship. Those guys are incredible: it costs them 500QR to sponsor a foreighner, and they sell them the visa between 5000 to 7000QR for 5 a five years visa plus 1500QR every year. Good buisness!!! Now I would not advise you to think of hiring one of those lovely girls cause even if everyonelse is doing it, it is illegal (an not everyone knows it!!). And you don't want to get into trouble with the Qatary justice. Yourself & your husband can only sponsor a person from another nationalty, so if either of you is Maroccan, it will be very difficult to obtain her a visa.
As far as her immigration visa is concerned, you can decide to have it processed by one of thoses agencies (advertised on Marhaba a sort of bible of information you can buy in any good supermearket around Doha), or have your HR department doing it for you. Unless you speak arabic (and mind you I understood the Northen African Arabic is very different from the Gulf's Arabic) I wouldn't dare doing it on my own. Also, I think she will need to take some medical exams in Marocco before coming to Qatar.
Roughly, it will take you 2 months to complete your own visa and from that point you can start your maid's application.
Now, big favour to ask you: would you happen to know anyone interested to come and work as a maid/ nanny for me??? If you know anybody you could recommend me I would really apreciate.
In anycase good luck with your new life here.