I was wondering how, even with the time and distance discrepancies, it was in any way realistic that...
... But then I looked up theories and calculations about the dragons, and the estimate is that they can probably fly at up to 200mph with a passenger
and even faster without. Now, how realistic it is for Dany to be comfortably riding a dragon at that speed without a windscreen, or at least a helmet / goggles (as apparently some open cockpit propeller planes did go at those sorts of speeds) is another matter. I guess you could assume there's some mystical / magical element that protects the rider from wind and G forces...