When you install from the Macbook Pro it will install drivers for the Macbook Pro, these may not work for the Mini. It is a bad idea to install an OS from another model.
Your best bet is to create a bootable USB installer & use that on the Mini to install…
Basically you download the OS installer on the Macbook Pro (get it from the app store), cancel the installer, then write it to the USB stick via one of these methods…
Create a bootable installer for macOS - Apple Support
Or use the app from DiskmakerX.com
Boot the Mini holding 'alt' at startup & select the USB stick - then run through the installer.
Otherwise you can probably use internet recovery mode on the mini…
About macOS Recovery - Apple Support
That will download a basic OS (to install from) & then download the original OS for that model. It's probably faster to use the USB stick method.