The only real answer is "it depends" for the correct way to do testing. You're never going to get out of thinking it through, there's no substitute for human judgement. If you care a lot about the memory profile of your data structure, you need to test that really carefully. But you might not care very much about that, in which case it would be a waste of time.

However, I think I can lay your fears to rest about "running a bunch of functions" - in the end all testing frameworks come down to running a bunch of functions. All that you get out of a framework is a (sometimes) shorter way to write those functions in a domain specific way. In the case of a data structure, a test framework doesn't buy you very much because the domain of the problem is basically "a computer program", which computer programming languages are pretty good at making statements about already.

So in short, it sounds like you're already doing the right thing.