Hi @ngreenberg,
I don't have much experience with Docker, but Qurro should be installable the same way as you'd install another pip or conda package into a Docker image. This is a nice tutorial showing how to use QIIME 2 through docker (albeit using an older version of QIIME 2). Following the steps for "Option A" of this tutorial, you should be able to just run pip install qurro to set up Qurro in your QIIME 2 Docker environment.
There are a few caveats -- one of these is getting Qurro to "stay installed" in your Docker environment, so that you can open this environment later without needing to re-install Qurro. This post discusses ways of doing this in the context of another package (phyloseq).
A second caveat is that Qurro used to only work with certain older versions (< version 2020.11) of QIIME 2. To address this problem, a few minutes ago I just released Qurro v0.8.0, which now supports all versions of QIIME 2 ≥ version 2020.11. (It's up on PyPI now, and it should be updated on conda soon.) So, if installing Qurro into QIIME 2 was giving you strange problems before, these problems should now be gone.
Hope this helps, and let us know if you have any further questions! :qiime2: