|The HP software must be installed, at least the basic "drivers".|
If the printer works (in Windows) , there is probably already enough software there for you to find the ink levels.
Control Panel - Classic view - Printers and Faxes.
RIGHT click on the printer model listing, select Properties.
Somewhere in there is where it will show you the ink levels.
You often need to click on a link to something not normally shown.
I can't tell you specifically what - I do not have a HP printer -
e.g. for my Canon printer you choose the Maintenance tab, then View Printer Status.
In other printer's properties there may be a Check Ink Levels selection or similar
You could always READ YOUR MODEL'S MANUAL !