I heard about the particular airline dumping their arrangement with a dog re-housing charity, sad sign of the times I guess.
Between selected destinations some breeds may be included as checked in baggage quite cheaply. However most destinations fall outside the few selected destinations, additionally a number of breeds are excluded from this service.
I recently adopted a 3 year old American Staffy and freighted her from PH to AS cheapest quote was $900 most expensive $1800.
Not sure what possible solution other than to talk to the airline and find out what caused them to drop the arrangement and try and problem solve that issue if possible.