The answers are a bit incomplete.
Even if QEMU and Docker use separate aspects of the system, they meet at the level of resources, such as storage and networking. The networking is especially interesting. Depending on your usage-patterns in this area, there are potential problems.
Things NOT to compound include advanced network filtering and aliasing, such as non-trivial firewall, and/or floating IP's, vlan and so on.
The result varies unreliable. You may be fine for a while, then one of the updates may contain a change that breaks it all apart. A new idea for how to filter firewall rule, a new network toolchain and so on.
Check your networking with
ip a. On my KVM hosts I see
vibrXXX bridges, on the docker VM I see
dockerYYY bridges. They typically get messed up with my
floatZZZ bridges and other stuff if I install both.
Make your backups and be ready to purge and reconfigure or reinstall.
I use 'desired state provisioning' to install my machines. This way I can always get from zero to full config in a matter of minutes, after commenting out the suspected culprit.
With a KVM host and a VM with Docker I kept them apart for years now, avoiding problems colleagues faced on the way.