New to diamond...
So I downloaded diamondqt GUI wallet from OP and installed it, fully sync'd the blockchain, encrypted the wallet, and unlocked it. I was never given any private/public keys during the process though; how do I obtain these keys?
If you want to export your private key, then you should first completely (not only for mininng) unlock your wallet.
After this go to the console and run the command:
dumpprivkey
The quotes (<>) are unnecessary! and copy the received private key.
But it's much more convenient and safer to keep a copy of the encrypted file wallet.dat.
Just copy this file when your wallet is off and save it on a safe medium (USB removable disk or USB flash drive)
To make sure that your copy of the wallet.dat file is fully functional, you can run a new DMD wallet with another location in the Diamond folder not
C:\Users\user Name\AppData\Roaming\Diamond
and put your copy of the file wallet.dat there.
To quickly change the location of the Diamond folder, I recommend to use this
description for convenience.
If your copy is fully functional, then you will see in your new wallet your balance

To verify the correctness of the password in you backup wallet.dat file, just try to unlock your wallet in the mode "for mining only"
P.s
Added this question and answer to the page
https://diamond-info.github.io/dmd_info.html