Pruning rowan after frist year growth

Rowan has a naturally open habit and if you want a tighter tree then yes you can prune it. I wouldn't remove all the branches, just shorten them or the tree may not survive. can you add a picture of your tree?

Do not prune back the trunk or you will have a hideous looking tree. We really need to see a photo of the rowan before we can suggest whether you prune or not... we have several and the only one pruned is because it can start to obscure the exit from our driveway.

I only like shaping trees in exceptional circumstances like Mg's

they have a genetic shape I think and look wrong when artificially managed.....
just me probably....

I feel sorry for it having to carry all those berries after very little growth, but I'm now inclined to think I should let it reach it's natural hight after which it should bush out. Just out of interest could I speed up it's growth by dead-heading the flowers for a season or two?

Rowan are, as SBG has already said, a very open tree. You are not going to get the dense canopy that you would with, say, an oak. There is no reason to deadhead the flowers the tree will not grow any faster. As a matter of interest do you know which Sorbus it is? If it is the wild rowan it will be very open in character.

You can take the berries off and lay them somewhere the birds can still eat them.
from the photo it looks like the wild form and it will thicken up in time but the open habit is natural for it.

Your tree looks to be doing well in it's first year, I would leave it alone personally.
I have a sorbus aucuparia asplenifolia which has been in my garden just over a year & still looks a bit straggly but has filled out from when I first bought it.
Plants often seem to sit still a year as far as top growth goes but are usually developing their root system.