Then I don't know what you're downloading…
I went to HP.com and searched for LaserJet 1300, whose results included a
Software & driver downloads link which led to Download drivers and software with a specific
Mac OS link that includes "hp LaserJet 1300 printing software and utility" which downloads lj1300macos9
Xen.sit
Stuffit turns that into "hp LaserJet Installer" which should run in X or 9 and launch an installer whose control pane includes "hp Laserjet Printing help"…
Letting that run should produce both the Installation Notes I quoted and an HP Installer Log File…
Was that not what you got?
That seems to be the right software set but it doesn't have any drivers - and going right back to the begining though it's no part of this ttest, which version of Desktop Printer Utility are you using that it could see any printer without a driver, please?