Adding a new printer (of the same model) to my MacBook Pro I bought another Epson SC P600 printer. I currently own the same printer that I have been printing from my MacBook Pro. The older printer is going to be donated. 

Do I have to uninstall the original printer's software and install software for the new printer? 

The new printer is the same model.
The short answer to this question is no, there is no need to reinstall the software. If its the same printer and the same model, the existing software will work perfectly well. 

The longer answer is maybe. I am not familiar with the Epson software itself but if there is an autoupdate feature you should be perfectly fine . Should there not be, I would, personally, reinstall the new software to include the latest updates.

If you have any doubt, reinstall the software just to be sure.