It seems that the USB communication to this printer does not work.
Alone lsusb does not work with it, and dmesg tells me something like "control timeout on ep0in"

But this printer is also not listed on HPs compatibility page:
http://hpinkjet.sourceforge.net/productslj.php\

Neither it is working with Mandriva 10.2

usb 1-2: usb timed out on ep0in
drivers/usb/class/usblp.c: usblp0: failed reading printer status

Use the foo2zjs driver from http://foo2zjs.rkkda.com

I used the new foo2zjs driver and this printer was detected and set up correctly on a fresh install of Ubuntu Feisty Fawn. It has printed everything I have thrown at it and has yet to fail me. For the price, I would recommend this printer to anyone looking for an affordable, Linux compatible laser printer.

After installing the foo2zjs package the printer is working under the followings SuSE / openSuSE-Distributions:

9.3 - works but sometimes it is needed to unplug and then replug the USB-cable or switch off and on the printer again (but this could be because the foo2zjs-package was older)
10.0 - works with the same limitations as on 9.3
10.2 - works without any limitations (with the newest foo2zjs-package)

ATTENTION! It is very important to get the HP-1020-files over the net (firmware) with the "./getweb 1020"-command! and do a "make install-hotplug"