Replacing HP all-in-one

I currently use an HP Photosmart 3310 for printing and scanning from a 2009 iMac and a 2011 MacBook Pro. I plan to change to an HP Officejet Pro 8600 Plus. Will it be necessary to uninstall the software for the 3310 before installing the new all-in-one?

No, it's not necessary. The HP driver for the old printer takes up very little space. It's best to leave well enough alone and just install the new drivers for the newer printer.

You can, however, simply press the "minus" button in the list of available printers with the old printer highlighted if you WANT to get rid of the old drivers.