Hamdelah you have been able to sort out the poroblems with the family etc. That is important. My recomendation is not to listen to all these negative comments about Qatar that some of the guys above made. I wonder why they are here if it is so bad. Let them go back to their own country & make space for people who appreciate a job & money here. Lets face it, if they did not make money they wouldn't be here, right. Unless they are stupid ofcourse, which wouldn't surprise me, looking at their comments!
Anyway, yes it would be better for you to get hired as an expat as you will get a better benefit package. Look at the many sites of contractors that are doing the hiring. This does mean that you can not come to Qatar on a visit visa... as a lot of the hiring is done via the internet anyway.
Good luck & welcome to Qatar
Aisha-Taweela