I have a GT which is a 2003 and a manual, so I have never driven an auto Aston before, I have driven Auto Jag's which share many of the parts.
The thing is, a whine from the rear would be the diff, however if it only does it in ONE gear then it has to be gearbox related.
The first step would be to have the transmission fluid drained and changed, also any filters that may be present as some auto boxes also have a filter.
It may be prudent to have all the drive belts checked as noises have a habit of being very sneaky in that what you may think is a noise form the rear, may very well end up being a noise from the front that is simply travelling under the car.
These steps above are service items that would benefit the car anyway unless you have proof these have been carried out recently.
It could even be the supercharger itself, obviously the loading on the engine and ancillaries will be different in 1st gear from the others.
So, change fluid / filter and all drive belts. If the noise is still present try and get it on a lift where you can go through the gears and have someone identify the specific area of noise before going any further.