No you can't. You can find that info at the OS level, or if you use the beta you could get at it via the Developer tools (since it's just a specialized browser window), but there's no userland option to export your conversation in the application.

That's why I wrote 'within Signal.'

As a simple example of how this could get messy, suppose I wanted to back up all my Signal messages, install a different operating system, install Signal there, and load up my old messages. I do have the IT skills to just find the database file and move it manually, but I'm only confident about that because I know its an SQLite database, where the keys are stored etc.

It's still an IT problem I would prefer not to have, vs the simple option of 'Do you want to export this conversation, with all the security implications Y/N' or 'Import this previously archived conversation?'