I have recently purchased a 2009 Audi A5 Quattro, and in looking underneath the car there does seem to be a place for a shaft to connect the front axle to the rear axle (which you would expect) but there doesnt seem to be any there... is this normal?
All Audi Qauttro's have a driveshaft that connects the front differential with the rear differential.
Your car does not have 4wd if it does not have a driveshaft.
In my country (Denmark) you can add the car to your profile at https://my.audi.com and add the VIN of the car. Then you can see all information about the car including factory installed options etc.
Check under the rear of the car you should be able to see the rear differential. it is the aluminium finned item between the rear wheels
If you don't have on then you definitely don't have a quattro, you should also check the VIN to make sure. The driveshaft it self is kinda hard to see depending on the angle.
If your car was sold to you as a quattro and it isn't then you definitely need to take it back.