MBIBABY I disagree with your statement that "you should be a muslim too". Wearing the Abaya and Sheyla has nothing to do with whether you are a muslim or not. Sorry.
I am an Australian and a Christian and out of respect for the Qatari women and men, I wear the Abaya when I go to either a shopping centre or to the Souq Waqif. If I am going to my hairdresser, then I wear my Western clothes but always fully covered.
I have lived here in Doha for over 2 years and I have received nothing but compliments and gracious conversations because I wear them. So go for it. Enjoy it.
You can get wonderful Abayas etc in the Souq Waqif. I just bought 3 last night! PM me if you would like a heads up as to where to get the best deals!
Good luck!