Which version of Bitcoin Core are you using?
If I want to change my password I use for bitcoin-qt, and not have old wallets with the old password jeopardize my coins, I can change password, generate a new bitcoin address and send all my coins to myself using the newly created address? Also this would refresh the keypool?
There is no such thing as a 'QT password'. There is wallet encryption via a passphrase, ergo you can use different wallets with different passwords (by switching out your wallet.dat file) on the same machine. If you change the password, then it gets only changed for your current wallet.dat, and not for the older/other ones.
I know I can make a new wallet.dat file, but that terrifies me! Read a few too many horror stories.
There is nothing to be afraid of. Move your current wallet.dat file out of the folder in to a safe location. Open Bitcoin Core and it will generate a new wallet.dat on its own.