I have had my last 2 children in Qatar and breastfed both, still breastfeeding my baby who is 10 month old.
We have to travel over an hour to get to Doha so I am always having to breastfeed while out.
So far I have never had a problem. I refuse to go to a public toilet to feed.
I have fed in Mothercare's changerooms. Debenhams Changerooms. Marks and Spencers at Landmark has a room, with change table.
I also will discretely feed in public, usually in a restaurant with a large baby blanket over me. (I have even fed in Home Centre and sat down on one of their lovely lounge suites for sale .... the baby wanted feeding there and then!!!)
I haven't really done anything different to what I did back home (Aus) with my other two children. However saying all this, Qatar has a long way to come to make it a breasfeeding baby friendly place.
When in Aus they have lovely "parents rooms" with curtained cubicles, automatic doors for the prams, drinking water, change mats, special nappy bins, microwaves etc etc. You will not find that here anywhere.
Good luck with the move