The W hotel is pet friendly but has strict guidelines. The animal has to be under a certain size/weight and it is expensive as you have to pay extra per night and a full room cleaning fee when you check out.

You can take your dog with you to Oman or Dubai but you would have to get the necessary export permit from Qatar, an import permit for whichever country you choose to visit, an exit permit from there when you leave and an import permit back into Qatar. You may also need transit papers for countries you are travelling through. All the vaccinations have to be up to date and if you are going to Dubai then I think your dog must have a microchip as well.