I'd recommend that you bring your own laptop and anything else you think you'll need. When you get here, you'll be dealing with a new culture, new place, etc. It sounds like you also need to find a place to live and a used car to buy. The last thing you'd want to do is to go shopping for a laptop, or anything else for that matter.

I also wish I'd brought more winter clothes. It's been raining quite a bit and the weather has gotten quite chilly. Check out http://www.thepeninsulaqatar.com/ to obtain weather forecast and plan appropriately.