It is really sad, especially at this time of year, when people leave Doha and some leave their animals behind to fend for themselves.
There are lots of people and rescue centres in Doha, trying to help the animals, but they are all over flowing with too many animals as it is. These rescue centres can only do so much and are dependent on people like you and me ,to donate any food,money or medicines to support them.
A lot of people try to help their own way and one thing you could do, is go back to the area ,see if the dogs are still around and if they are, leave food and water for them.
I agree with you that it is very expensive to take a pet with you when you leave, but this is the criteria of the airlines.
You can go to the government vet and get vaccinations and exit permit for your animal,Without charge, but you must still pay the airline transport and buy a special carrier for your pet.
It would be really great if the airlines did as you said and let you use your excess luggage allowance for your pet, but this will never happen. They would loose a very lucrative business.
Shame!