Carpet isn't going to damage the PSU (I assume it's not 50 years old and failing apart) the fan isn't going to be strong enough to clean your carpet.
Also you'll probably get way more dust coming in the rest of the case from other case/psu fans and falling down into your PSU, as most of the dusty air in your room is going to be above foot level. Once dust has settled under you case it's likely to stay there, only dust in the air tends to get into your case.
Face down is the ideal way to have the PSU mounted, and the reason why the case has a ventilation mesh.
Since heat rises you fan will be trying to counteract thermal dynamics (and it won't be very successful at this, as it's not been designed to run that fast). So a lot of the heat will rise into the rest or your PC, rather than being vented out of the back of the PSU.
Easy way to show this, put your had above the PSU when you are benching for extreme power use and if you feel any temperature difference the PSU fan isn't running fast enough to counteract thermal dynamics.
As far as I'm concerned the only reason to have the fan face up is if the case you have would completely block it off. Mostly likely this would be an old or cheap case as most of these designs have been mothballed.
If I had a case like this I'd bin it or use it on a cheap non-gaming system only.
So don't switch, it's definitely not the safe side unless you want the PSU nicely insulated with case dust.
