The Cady is a fun little moped for kicking around, but you'll be hard-pressed to coax it past 40 KPH. It was more or less designed to prop up on the back of a Winnebago and to buzz around campgrounds. It is a very limited design as for speed/power. From what I can tell there are absolutely no performance parts available for bolt-on horse power. And as for re-gearing, this will not accomplish any speed increase as it will require more torque to reach your max RPM. However, if you have some 2 stroke tuning skills you could always try some creative ways of increasing the charge of air/fuel in the combustion chamber, or possibly modify that super restrictive exhaust.
There is a guy on the mopedriders.org site (rebelrob, I think)that has managed to transplant a Motobecane AV7 engine onto his Cady. That engine has quite a few bolt-on accessories available and will likely be your only real hope of getting any power for that bike.
However, your best bet is to just get that thing running as well as you can and just enjoy it for all of its limited capabilities. And if you are looking for a speedier ped, do consider upgrading.