I do have a backup domain controller but do not currently know how to configure file replication on it. (I understand this is possible also)

Generally file-replication doesn't really give you a very useful backup. Yes it will help if all your drives die in the main server, but if someone deletes something that shouldn't have been deleted that deletion will be quickly replicated from your main system to your backup.

You should have at least one backup, and preferably more, at any given point in time that is completely offline and separate for your production system. That way if something catastrophic happens you will still have a copy of your data that is safe.

I am looking at setting up a backup solution... well including in my backup solution actually... an external harddrive on my main file server. I then use something like Microsoft SyncToy to 'sync' data onto the external hard drive.

Copying your files to a portable drive seems like a useful solution. I suspect I would script a backup with robocopy instead of trying to use SyncToy. SyncToy doesn't really seem something I would want to trust my backup too. You really shouldn't even need a full sync, since during normal backups your data should only be going one direction.