Generally, AN's grow 1 or 2 mm a year, but sometimes the growth is faster.
There is no rule about what size dictates when treatment should begin unless the tumor is very large and exerting mass effect on the brain stem and cerebellum.
Treatment usually is recommended when symptoms require it.
Diagnosis is a difficult time, but your tumor is very small and you have many options available to you. Your tumor may never grow, and if it does, radiation will one choice so surgery is not necessarily in your future. The choice will be yours.
If you are confident in your doctors level of experience, see what happens in the next year. If you are less confident, you can always get a 2nd opinion from a doctor experienced in treating AN's.
The more you learn about the tumor the less frightening it becomes. There is good information available from the association. Good luck.