You are going to have to do at least some initial setup with a real monitor. Once you have got the normal desktop you can then turn on Screen Sharing and thereafter use that to remote control the Mac over the network.
The Mac mini comes with a HDMI port so you could possibly use a TV to do this initial setup.
If you have no external keyboard (even a Windows USB one would do) then you have no way to boot the new Mac mini in Target Disk Mode.
If you have a keyboard and can boot the Mac mini in Target Disk Mode then you can do the following -
- Boot the new Mac mini in Target Disk Mode by holding down the T key
- Connect it via either FireWire or Thunderbolt cable to the MacBook Pro
- Tell the MacBook Pro to boot from the Mac mini which will act as external hard disk drive
- The MacBook Pro screen and keyboard will then be in use but you will be configuring the software on the Mac mini hard disk
- You can then turn on Screen Sharing
- Shutdown the Mac mini and thereafter do everything via Remote Control