You can't use QR if it has track ends, aka horizontal dropouts. EBB with vertical drops is fine with QR.
And to the OP - no, you need to get a new hub/wheel as you cannot convert a solid axle on a track hub into a hallow axle which is 1/2 as thin.
MIN is right about not using QRs on track ends because of axle slip; however, you can overcome this using tensioners.
MIN is wrong about needing a new hub/wheel. it's possible to convert bolt-on axle hubs to accept QR, though this takes a bit of work and parts. i'm in the process of doing this myself.