You can take a small dog IF there is no one else taking them...There is a limit per cabin. Why can't you promote the rescue/shelter in the places where the dogs are? I don't understand the need to transport animals. I see pax sneeze and complain about animal fur/dander/allergies. Not to mention the barking--or is it ok to drug them. I personally have issues with animals in passenger compartments.
What is the "humanity" when putting animals in carriers and traumatizing them for several hours? What about large dogs? Who's willing to pay for the cargo space? Are they no less worthy of being saved? What about cats? Are they not worthy of saving?(bet there will be lots of comments! haha)
Makes more sense to assist local shelters (especially the no kill ones) with better means, like fund raisers, donations, etc. This is my personal opinion. I sympathize with your cause but have no empathy in the logistics nor the necessity. I hope you do well with your rescue mission. Have you contacted DL?