Lean as suggested, check your airspace (even if controlled, they'll probably give you a clearance of you ask), avoid moisture, and go for it! As mentioned, for the sake of the engine, do not get up there, and close the throttle. Presuming this is a fixed pitch prop aircraft, once you reach to top, plan to reduce RPM at a rate no greater than 100 RPM per minute, as you start down. If Constant speed, 1" MP per minute. Descend with some power on, and the slowest practical airspeed, to reduce the cooling of the engine, which will now be producing little heat in the cooler air. By caring this way you are preventing "shock cooling" and the person who pays for the maintanence of the engine will appreciate it!
During a flight test for MOGAS, I once had a normally aspirated Cessna 180, with a carburettrd engine, to 20,800'. At that altitude full power was only about 40% of sea level, and the maximum attainable airspeed was stall speed. I regularly fly longer routes in my Cessna 150 at 9,500'/10,500' when the strong tail wind becomes an advantage.
Have fun, Pilot DAR