Check with the airlines, they know exactly what you need to export a dog from Egypt to Doha. Some may not transport any animals at this time of year due to the heat. You will need a vet report from the Egyptian Dept of Agriculture usually within 10 days of travel, all vaccination certs etc. You will also need an import permit from Qatar - a pet relocator can help you with this.

You cannot walk your dog on the Corniche or Sheraton Park it is prohibited.