The trick is to make sure your propeller blades are deployed. I spent way too long trying to figure out why my plane wasn't moving despite the fact that my propellers were spinning.
Made some tweaks to the design, then I strapped some rockets to it and put it in orbit. I refuelled it at Kerbin Station and attached a heat shield to its front shielded docking port, and now it's waiting for a transfer window to go to Eve.
