Bluey, you'll have a problem with Tex's option. I live in DB as well and you can't take the dog on the bus from the airport and you can't take a taxi into DB, so short of hiking over the mountain from Tung Chung (which can be done, but would require a LOT of effort) you're going to need someone with a vehicle to deliver the dog to you.
Now that I think about it there's a Merc van that you can hire to go to the airport that will get your dog...I think it's ~$200HKD to hire that for the trip...you could bus out and then schedule a time for the Merc to pick you and your dog up.
We used Export-a-Pet and had a great experience when we brought our dogs from the states. They got in a day before us, stayed at a kennel overnight and were delivered to our door the next morning. For ease of use you might consider that option: http://www.export-a-pet.com/
I don't recall it costing that much to have them picked up and brought through customs and boarded overnight...I think it was around $1400HKD for 2 dogs...this was a drop in the bucket after paying $4000 USD to have them shipped over!