Another option is just relaxing in the F class lounge. There are private bedrooms with ensuite bathrooms there as well, although you might have to wait 2 or 3 hours to get one. Until then the lounge is very comfortable.

The Dubai airside hotel is very convienient but very expensive. I have tried it a few times, because some of my travel companions did not have a visa for Dubai but I don't think I'll do it again.

The Le Meridien is right outside the airport (more or less ,) and you will get a free car to and from the airport so it should be painless.

Cheers