You can find the 2019 installer on Intuit's web site (I'm not sure of the link but I've posted it before - Im on a different computer today).   Then you can just install 2019 on the older machine. When it prompts for the license number and product code use the same ones you used to install 2019 previously (these are visible in the QuickBooks->About menu on that machine). 

Then you'll be running 2019 on both. You are allowed to use the same license on two machines as long as you aren't working on the two at the same time.  Which is exactly what you need.