sounds a bit like its running lean (not enough fuel), seeing as it idles fine then the pilot jet should be clear, try cleaning out the main jet.
now, removing the carb on the DT is a lot simpler because theres no plastic to get in the way, im unsure on your particular ped but you may need to remove the airbox to get to the carb itself and then undo any nuts/bolts which hold the carb onto the reed block (back of the engine).
once you have the carb off, turn it upside down and undo the four screws on the bottom and remove the float bowl. you should now see a little brass screw with a hole in the centre on the end of a small shaft sticking out of the carb body, check the hole is clear and free from any dirt which may restrict the fuel flow, use a nylon bristle from an old toothbrush or carb cleaner (or for best result use an airline to blow through it).
this should solve the problem, if not, its probably something else