I test drove one and had the same experience so you're not alone.Pretty sure it was the 1.3 MHEV with the "xtronic" box, performance once on the go I thought was very decent for its size, just the initial go it just seemed to take a second to think about what the acceleration pedal is when I pressed it, and overall just a jerky experience.
I'm also pretty sure they've done away with the DCT now for all their cars, the DCT was on the previous gen Qashqai when it had a facelift and the 1.3T engine
Turn eco mode off and it doesn't happen though! You do have to turn this off each time you get in the car.