You probably always play mage?
A paladin game I started (and stopped when I realized his ultimate resurrection skill does not support no-loss run) had the pet dragon at level 22 when the paladin was at level 15. Same with the warrior game I have right now, level 17 warrior and level 21 pet dragon. But leveling the pet dragon is not really that big of an issue, unless a level 60 pet dragon is also one of your target goals.
Oh no... for a game that you want to target level 60/high score you should really use the KBScanner to make sure that you have at least 3 ancient knowledge scrolls being sold or as treasure pick-ups. Then pray that you get at least 3 more from duplicate navi maps and dragon dig.
If you have read other posts, ancient knowledge scrolls are critical for a high level and high score run. And there is absolutely no guarantee you would get them in great supply.
It would be very frustrating to be in the mid to late game and still not know if you could reach level 60 simply because you don't have enough AKs. As painful as it may seem, I would suggest restarting the game. If you do restart the game, I suggest making sure you have 3+ ancient knowledge scrolls and 2 hand of necropolis at the starting islands (in my game, I got them both at Verona).