It's good to see you here again, MandyAZPCP.
Let me address your concern with installing QuickBooks Desktop (QBDT).
There's no need for you to install QBDT 2019 on the old computer. You can directly install the software on the new computer and create a backup copy of your company file in the 2016 version.
Then, copy the file using a flash drive or other external devices and restore it on the new computer.
As a reference, you can check out this great article for further guidance: Move your company files to another computer.
That should do it. As always, you can reach out to me if you have further questions by leaving a comment below. I'll be here to help.