I don't think you'll be able to go to a dealership like Honda or Toyota and buy the hybrid model of the Civic or Pryus but I did see Ford Escape hybrid at Al Aweer once and a Honda insight driving on the road. I'd worry though, even if you were inclined to import one in, how easy would it be to service?
Maybe you can compromise a little, like for example:
1. instead of getting a 4X4, get the same model in the 4X2 version (i'm assuming you'll be driving mostly on the roads)
2. Don't get a car that is too big for your needs (I disagree with the whole "bigger is safer", read any safety magazine and you'll know this is far from the truth)
3. try reorganizing your errands so you go to one area of the city once instead of back and forth.
4. Drive slower
(please not in the left lane)
5. Take public transport, okay busses suck but there are share taxis and the like that will save you tons and are a viable option if you are living in a community where many people commute to a similar destination.
6. Ride your bike, except in Sharjah where it is a felony
, weather is getting quite nice. (I use to walk to work when I lived in the city, a nice way to start the day)
Because gas prices are moderate compared to many parts of the world, you can get really nice/bigger cars for likely cheaper than you can in your home country, the lack of government support/infrastructure to support alternative fuelled vehicles make it not a feasible option for many.
Good on you for at least thinking about it though.