Assuming you want the service management aspect of docker compose look at user-mode process supervisors like supervisord. You can install it in your nix environment and config all the dependent services it should manage. It's a little more crufty vs. the simplicity of docker compose but it also has a lot more power and flexibility. There are tons of other options to explore too like systemd user services or skarnet's s6 suite.

What I really want is to be able to do things like spin up an isolated postgres instance to run my unit tests against, with zero config on my part except specifying a postgres version in my "docker-compose.yml" equivalent.

+1