Yes prune it as soon as you wish. Remember if you have a rabbit problem cut it fairly high, at least two feet as they will eat the new shoots. :o
If it is still a single stem do not cut too low, you need some stem for the shoots to flush from.
Hazel coppicers start low and each year cut a bit higher by necesity.
The more stems you leave the more buds will flush, just a couple of stems will send up tall lank growths.
Corulus avellana the common hazel used to be layered by the coppice growers. I would imagine you may be able to grow the nuts. Not sure about cuttings, I doubt they are very sucessful as this would have beemn easier for the coppicers than layering. :)
Have fun. :D
I grow a common hazel and a purple filbert and coppice each one on alternate years for pea and bean sticks, bird perches and sticks for perenial supports. 8)