Get your taxes done using TurboTax

You don't need to re-install TurboTax on the old computer.  But you do need to copy the TurboTax file of last year's return from the old computer to the new one.  If you're not sure where it's saved to on the old computer and do a search for it, search for a file that ends in .tax2017

Copy that file to the new computer and when starting a new return on the new computer, select the import option and point it at that .tax2017 file.