is 11.7mph a good average speed for a 13 year old on a road bike?

If you are asking as far as safety is concerned, yes, that is a good speed. If you were to have an accident, you wouldn't be going too terribly fast and probably wouldn't be badly hurt.
 
Are you putting in a lot of effort? The key to getting faster is just riding with hard effort, but you need a slow ride after every fast rid, to recover properly, and be stronger for the next ride. When I was 16, my avg was between 14 and 15. Now my average speed is over 18.
 
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