If you are trying to compile avogadro 1.2 from source and following instructions from (Compiling on Linux and Mac OS X - Avogadro). The link to download qt4 doesn’t work, neither it is available on the official site. You can download it from apt. Just open terminal and run command sudo apt install qt4-dev-tools.
You clearly state your experience relate to work within Ubuntu 20.1/Mint20.1qt1.
My observation, complementary to yours in Linux Debian 11 / bullseye, testing however is that this does not work (any more). The query for qt4-dev-tools in the package tracker reads like it transitioned into more senior branches (reference).
This is kind of sad for that the version of the program available as such from the OS’ repositories is of the Avogadro2; contrasting to Avogadro still lacking e.g., the entries to quickly set up computations with other programs (mentioned e.g., in an earlier manual to sit below extensions).
We’re happy to help provide packages wherever possible, and to help those who want to help package (e.g., @kevinsmia1939 spent a lot of time and effort in creating a Flatpak).
I personally don’t know what to do as far as the Ubunutu packages. If someone wants to help us test alternate packaging, I’m happy to investigate. GitHub provides free cloud compile, which we’re using for nightly binaries.