Does Time Machine support APFS? I just updated to macOS High Sierra. What's the best way to use Time Machine under Apple's new APFS file system. Should I use Disk Utility to convert my external Time Machine volume to APFS?
Time Machine supports APFS as a source and not a destination. You can't backup to an APFS destination disk and Time Machine will inform you that the disk needs to be HFS+ if you attempt to do this.

Right now, there's nothing you need to or should do. Your internal disk has been converted to APFS and your backup disk is still on HFS+, so Time Machine will function as it always has, and will continue to inherit previous backups despite the difference in format. On a future date when Time Machine supports APFS destinations, you can convert your backup disk.