Your drivers will remain on your computer, all you do by clicking the - key is just eliminating that printer from your choices of installed printers. Clicking the + key just (hopefully) re-installs it.
One last thing did you download and install this update:
http://support.apple.com/downloads/HPPrinter_Driver_1_11
If you haven't yet I would strongly suggest doing so using it's the most up to date drivers currently available from HP the LJ 1012 is listed in it as one of the supported printers.
That should do it. I have my 1012 set as Shared and use Bonjour on my HP notebook to make the connection. Printing on the notebook also works just fine. Not that it matters but I also have a Officejet 7410, and Color Laserjet 2600N that all work perfectly on my iMac and Windows machine.