Do you have to have a CDL to drive a single axle dump truck with air brakes?

Depends on the gross weight rating. If it's rated at 26,000 lbs. and below (such as a Ford F650 or F750), no, as long as you don't go over that weight. If it's a vehicle rated at over 26,000 lbs, then you need a Class B CDL.

Now, if you take a truck rated at 26,000 lbs (which you wouldn't need a CDL for), then add a trailer, you've created a combination with a GVWR of over 26,000 lbs, and you would need a CDL for it. If the trailer is rated under 10,000 lbs., you would need a Class B CDL. If the trailer is rated over 10,000 lbs, you would need a Class A CDL (the same licence you would need to drive an 18 wheeler).

So, basically, for a few examples:

26,000 lb. truck with air brakes = No CDL required

30,000 lb. truck with air brakes = Class B CDL with air brakes required

26,000 lb. truck with air brakes and a trailer of less than 10,000 lbs = Class B CDL with air brakes required

26,000 lb. truck with air brakes and 15,000 lb. trailer = Class A CDL with air brakes required

10,000 lb. truck with 15,000 lb. trailer = No CDL required

10,000 lb. truck with 20,000 lb. trailer = Class A CDL required (no air brakes necessary if the vehicle is not so equipped)

Bear in mind that these are for gross vehicle weight ratings, not the actual weight of the vehicle itself. So, if a truck weighs 10,000 lbs. empty, but has a gross vehicle weight rating of 33,000 lbs., you need a CDL to operate that vehicle at all times, regardless of what the actual weight of it is at any given time.

There is no actual air brake endorsement for CDLs - if you don't pass the written portion of the exam and test in a vehicle equipped with air brakes, you get an L restriction.