I would like to know more about this for future reference. How costly are we talking? How big of airports are necessary? Or is it any airport Delta flies to?
Just do a Google search for "delta live cargo" and read up about it, it looks like the rate for birds is a minimum $180... Rates have went up quite a bit since I used to do it, but it's still cheaper than driving and as I said they get proper 'live animal' care doing this, they are not treated as just another box...
It's been years since I have shipped this way, but assuming things have not changed to much there were two ways to ship... Obviously both parties need to have an airport that Delta cargo services, other airlines might offer similar services but when I was in the business everyone used Delta... There were two types of shipping, one was regular animal cargo and it what I used most of the time, basically the animal is dropped off at the cargo loading docks (usually off site not at the airport proper) and then picked up at the cargo loading docks at the receiving airport... The second 'premium' service I believe is their 'DASH' is you take the animal into the airport and drop it off as basically 'luggage cargo' and then it's picked up at the other airport in the unclaimed luggage area... I only used the premium service once as it was obviously more costly but also a hassle to find parking, go into the airport, get the package and what not, much, much easier to just pull up to a loading dock off site (no security hassles or parking hassles) and grab the package... The only real advantage to the premium service is you know when the package will arrive because you get a flight number, for cargo you have to wait until they call you and tell you it arrived...
I used to get animal shipments from Miami, FL every week to Chicago, IL and it generally only took about 6 hours from the time they dropped off until I picked up as long as the animals were shipped in the morning, if it was shipped later in the day it sometimes got stuck overnight at Delta's Atlanta hub, and arrived the next morning... Cargo is generally not given priority or a specific flight (unless you use the premium service) regular cargo is put on whatever plane has room so it might take a few hours before it catches a flight, so it's always best for the seller to drop off as early as possible if you want same day delivery...
Oh and BTW if you are squeamish be prepared as funeral homes use airline cargo to move bodies around, so it's quite common to see a bunch of caskets on the loading docks... Didn't bother me but I was caught off guard the first time I made a pickup as saw all the caskets just sitting on the dock...