You cannot use the older dirve in the new Mac Mini. The new unit uses a special OS X system that is unique. You need to start your new system up and migrate your files from your 2009. Once this is done use carbon Copy Cloner or similar to clone the drive back to your SSD (use external hook up) then install the SSD.
Your warranty will NOT be voided. See below from the Mac Mini Product Information under Do Not Make Repairs Yourself. So, you're OK to make other changes, but if you damage your Mini during the process, your warranty will not cover that damage.
If you install items other than memory, you risk damaging your equipment, and such damage isn't covered by the limited warranty on your Mac Mini.
I would do a Disk Utility restore from your new Mini's HDD to an external drive. Boot the Mini and press Command+R to boot into the Recovery HD where you can use Disk Utility to do the restore. After you change out the HDD with your SSD, boot into your external drive's Recovery HD by pressing the Option key at boot time and selecting your external drive's Recovery HD. Now do a Disk Utility restore back to your SSD. I did this on a late-2012 Mini BEFORE I ran setup. It all fit on a 16GB USB thumb drive. So, now I can always restore back to factory condition without having to redownload OS X.
The Disk Utility restore does a complete clone including the Recovery HD. Carbon Copy Cloner will clone the Recovery HD also if you tell it to. Some people don't know that and after they clone their OS/apps/data to a new drive, they discover the Recovery HD is missing.
You cannot use the older dirve in the new Mac Mini. The new unit uses a special OS X system that is unique.
Brthtththththtth! What a load of cod's wallop! Just stick the hard drive in and away you go. I put a hard drive into one of my iMacs that had XP installed on it and it booted up.
Warranty? What's that? If you do any modifications except for the ones specified, which vary from model to model, of course you will void your warranty. Most warranties only cover a RAM upgrade as user serviceable upgrades. Just carefully check your model specific warranty and see what is covered.