Finally, I am able to print to HP LaserJet 1020 from my Linux machine. Thanks to the guys at http://foo2zjs.rkkda.com/.
Just follow the instructions in the INSTALL file, you should be able to successfuly print. One thing I was unaware was to control CUPS via web (in my case, browse to http://localhost:631). From there, I could then test. Although I've tested remote printing, it shouldn't be a problem because CUPS will handle all!