Hello Jarl,
Welcome to the world of DOUGLAS! It looks like your bike is already listed in the LDMCC machine register. It appears that you may have misquoted your frame number - frames with the prefix 'AE' only had 3 digits - the entry in the register shows frame number AE291 with engine 5/L 181 as being a 1936 500 Aero. You will only find out if it is still a 500 when you take the heads off, as 500 and 600 barrels are interchangeable, with no external differences.
From the machine register, only 19 of the 500's seem to have survived, along with 12 250's and 9 350's - the rest are listed as 600's. Irrespective of capacity, all Aeros used the same cycle parts to house a variety of engines and gearboxes.
Regards,
Eddie.