I think that in life you need to try everything once! Shaving off one’s hair can be one of the most liberating things they ever do! You are definitely not too old!
Just a few things you need to make sure of:
Your head shape at the back should resemble the shape of a question mark. If you have a head shape that is too flat at the back it can look funny.
You also need to take into consideration your face shape.
I would recommend going into a salon and getting a consultation which is normally free of charge.
Also check out a website that has a virtual makeover section, where you can place different hairstyles on a pic of yourself. That will give you an idea of what you will look like.