Please excuse the following detailed response, as I feel it is both necessary and will be helpful. Also, it looks like I made a false assumption above, as apparently you are not using SuperDuper!.
What you are describing will be the use of the OS that is on the Mac Mini, as Migration Assistant does not copy the OS itself (nor "other" OS-related files). As I mentioned above, your new Mac Mini will most likely come with El Capitan (or maybe Sierra?). (By the way, as you will be getting the machine with an additional 4 gig of Ram, are you getting it from Apple? If so, then there is a good chance that it will come with the latest version of Sierra, OS 10.12.1 (OS 10.12.2 is currently in beta testing)). It will be important for you to 1) have the file entitled "Install OS X El Capitan" or "Install macOS Sierra" on the Mac mini in a couple of locations, and 2) insure that any third party apps you have on the iMac are compatible with the newer OS. There is the possibility that you would need to install those updates after all the "stuff" is on the Mini. For example, I use Onyx and a Logitech mouse, on both of my Macs. I already have the Sierra updates for both Onyx and the Logitech Control Center software, but when I upgrade from El Capitan to Sierra, it will be at that point that I install those updates, as they will only work with Sierra. Contrast that with SuperDuper!, as V2.9.1 (the latest) works with any Mac OS from 10.8 and above. As it is, it seems like you are using Office 201X already. Is that Office 2011, or Office 2016? For either of those, it would be best if you have the latest version. I myself had been using Office 2011 (including Outlook 2011 for my EMail needs), and I always kept it up to date. But, Microsoft will (most likely) stop supporting Office 2011 in the "near" future, so I have already obtained and installed Office 2016 (including Outlook 2016, and the "transition" from Outlook 2011 to Outlook 2016 went very, very smooth, and in fact, was basically seamless), including the latest version. It works fine with El Capitan, and I suspect the same will be true with Sierra.
But, as long as you understand all that, and make those preparations, that is a good plan. Assuming you are successful, that will give you a fully functional Mac Mini.
I already mentioned above the differences between SuperDuper! and Carbon Copy Cloner. I believe there are 1 or 2 other backup/cloning programs out there, but either SuperDuper! or Carbon Copy Cloner is an excellent choice. I can tell you for a fact that SuperDuper! does the job, and there have been a couple of instances where having a bootable backup "saved my bacon", per se. Also, I have recently (for the last two Mac OS upgrades) started with the upgrade of the Mac OS from the bootable clone, for both of my Macs. If you are "uncomfortable" with not having the (hidden) Recovery HD partition backed up, then use Carbon Copy Cloner. Given that I have mentioned this a couple of times already, here is a link that describes how to boot to that partition, and what you can do with it:
https://support.apple.com/en-us/HT201314
Sometimes, that partition does not get created on a clean OS installation. But, that has never happened to me. Also, the version of Disk Utility that comes with El Capitan and Sierra no longer can Repair Permissions. Again, though, for me that is not an issue, as the excellent freeware program Onyx has that feature (as does TechTool Pro and Disk Warrior, both of which I have).
Again, as I stated, not having a backup of the Recovery HD Partition is not an issue for me, as 1) it gets created with a clean, "virgin" installation of the OS, 2) there are other ways of creating it, and 3) I have a couple of more advanced disk maintenance/repair programs that are superior to Disk Utility. (The free program Recovery Partition Creator (
http://musings.silvertooth.us/2016/05/recovery-partition-creator-4-0-1/) can re-create that hidden partition, but it requires that you have the file entitled "Install OS X El Capitan" or "Install macOS Sierra" that I mentioned above. Also, I have not used it in a while, so I do not know whether it will work with Sierra).
SuperDuper! costs $27.95, and Carbon Copy Cloner $39.95. These links explain the capabilities of each program:
SuperDuper!:
http://www.shirt-pocket.com/SuperDuper/SuperDuperDescription.html
Carbon Copy Cloner:
https://bombich.com/
Now, after you do this, there will no drive inside the iMac, is that correct? Also, for the 1 TB 5400 rpm drive that you will eventually put in an external case, if you do decide to purchase either SuperDuper! or Carbon Copy Cloner, you can use such software to make a backup/clone of the stuff on the Mac MIni to a partition on that drive. That is what I did after I did the swap, although I was backing up/cloning the stuff on my MacBook Air to a partition on that drive. The other partition contains miscellaneous "stuff", including movies and TV series. It comes in handy when we travel. Just be aware, though, that booting from that drive will be slow, no matter what type of connection you have. The 5400 rpm speed is really slow!
As for 4 Gig versus 8 gig of Ram, I actually can upgrade the Ram my self on the Mac MIni model I have, but given that the Ram is now soldered onto the logic board, that's a wise choice. Having "too much" Ram is never a "bad" thing. I have yet to have a need for more than the 4 gig I have, but then I keep my Macs "lean and clean", and rarely run more than one program at a time. For example, as I am entering this, I am only using Google Chrome, and i still have about 1.81 GB of free Ram.
OK, I think that's it. Again, please excuse the long post. I hope it is helpful!
Happy Thanksgiving. And don't eat too much turkey!