1. You should be able to get a nice villa, 3-4 bedrooms for that amount. Check out www.gulftimes.com, they always have advertisements. I think everything in Doha is around 20-30 minutes drive depending on time of day.

2. Buy at least 5 heavy duty transformers/adapter and extension cords with multiple outlets from your current location. Outlets here uses different prongs.

3. Qatar is under REGION 2, you should be able to buy a multi-region DVD player here. They cost around $100 - $150.

Qatar is a very safe place except when your on the road driving... :D