Well I can tell you how to get some more speed, but it requires some work. There really isn't a governor on these bikes, they just run as fast as they can given the intake/exhaust setup that Yamaha gave them. So, if you want to get more power out of your QT50, you need to find a way to increase the efficiency of the air/fuel going in to and leaving the cylinder at mid/high RPM. Keep this principle in mind. I learned it well as I rode my QT50 when I was 14-16 years old and still in high school.
I consider myself fortunate as my dad was very knowledgeable about how 2-stroke engines run and what you need to do to make them "breathe" better. One simple mod that we started off with was to take the airbox (the black box with a filter inside clamped to the back of the carb) and drilled 4-5 3/8" holes on the back of it. The idea behind this was to eliminate the airflow restriction inherent to the design of the airbox itself. Picture the maze that the incoming air had to follow just to get to the carb. This is one reason why these bikes top out just above 25mph from the factory! Now imagine what happens when you put these holes in the back of the airbox. Now the air can flow in from the back of the airbox, straight through the filter and into the carb. (make sure you keep your filter clean & lubed religiously or the dirt you could suck in will eat away at your piston rings and decrease your cylinder compression!!) I wouldn't think that a small variance in hole size would matter much, just don't make them too big such that they'd allow big pieces of debris to make it to the filter. Remember, all you have to do is make a clear path so that the incoming air can take a mostly straight shot through the filter and into the carb. Just from this mod, I gained power throughout the RPM range, and I was able to leave other QT50s in the dust off of the line and at top end at will...even in instances where I was 40-50 pounds heavier than the other rider. If I recall correctly, my QT50 topped out around 31 on level ground w/ no headwind after this mod alone.
The next easiest thing that you can do is slap on an expansion chanber. I got a mid-top end pipe from DG that was made for the QT50. Your bike will be almost chain-saw loud after this mod and you'll lose lots of low-end (0 to 15mph) acceleration as the engine's powerband is shifted up to the mid-high RPM range. Once it gets on the pipe though, hang on! When I grabbed a handful of throttle when on the pipe (anywhere above ~18mph for mine), that tiny chainsaw motor meant business! What a ride it was! I can't believe that my county/town cops never approached me concerning its legality in my state given how much louder it was. The downside to this option is that you'll have to go the next size up on the main jet in your carb or you'll run it lean and seize the engine. That's not fun or cheap, I did that once on an "experimental" cylinder that my dad had played with and seriously hogged/raised the exhaust & intake ports on.
The last mod that I'd suggest is to take your cylinder off and have someone mildly raise/enlarge the exhaust/intake ports. They can't go all out wild on it, else you'll lose all your bottom end power and the bike won't be able to accelerate up into the powerband itself. They just need to make the cylinder "breathe" better at mid/high RPM. Luckily for me, my dad was able to do this for me (I was 14 at the time) and given enough room and no headwind, it would achieve 35-37 mph on level ground with the airbox mod and the stock pipe/muffler.
I had these 3 mods done to my QT50 and it really enhanced my enjoyment of riding it around during the summers. I put perhaps 15,000 miles on this bike (the plastic speedo/odometer housing in the front hub failed after about 9,000 miles due to these speed mods), and I cannot stress enough of the importance of taking care of your air filter and making sure you keep that oil reservoir full. I never ran into overheating problems, nor did I ever have a mechanical breakdown because I kept up on its maintenence. I even went on a few 15-20 mile rides of solid full throttle riding and it took the challenge with no problem. Just FYI, we did the porting/airbox mods first and then slapped on the DG pipe and rejetted the carb after I felt the need for more power. In the end, I was able to get the QT50 consistently up into the 35-40 mph range even on slight uphills, and I was able to almost hit 50 going downhills and also by catching a lucky draft from an SUV on level ground (which was probably one of the dumbest things I've done in my life so far). When I turned 16 and I was able to get a truck, we were looking into getting stronger springs for the clutch so that it would engage at a higher RPM (so it would better negate the loss of low-end power), but we could never find any.
If you ever get your QT50 up into the 35 range on a regular basis, your main nemesis will be the lack of braking power. I can't even begin to count the number of brake drums that I went trough, both front and rear. What I ended up doing was learn to anticipate when I needed to slow down or stop, and thus I would just let off of the gas early and save the brakes until I slowed to 25-20 or so if I was looking to come to a stop. This cut down on the brake bill dramatically.
Well, I hope you and others find my experience useful. It was a heck of a lot of fun and cheap transportation for me before I could get a car...if you have any questions or comments please feel free to email me!