I would imagine that the 12gig of internal space is probably a small Solid State Drive that fits into the 2.5 drive slot vs. being separate memory and leaving the hard drive slot empty.
Just in case, what I would do first is take a USB Hard drive and use it to back up the system.
Once it is backed up, if I remember from when I installed my second hard drive into the PS3, the case itself has the brackets that are needed to be installed. You shouldn't need external hardware like trying to slap a 2.5" drive into a 3.5" drive in a PC.
You may expect to see the SSD in place, if so take it out and put in your new drive. Then go through the process of restoring the data to the hard drive using the backup you made.
If there really is no hard drive in the system, then you should be able to put the new one in and then you should be good.
I did this with a launch-PS3 vs. the new slim model, but I would not expect much to be too different since the OS is still the same.