Should I repair this very small area of minor water damage on my bathroom floor?
If your subfloor is wood, I would verify that the wood is in OK condition.
Caulking is good, but it's not necessarily a solution here. You have a piece of wood trim by a major source of water. That trim will get wet sooner or later, caulk or not. What you should look into is getting some vinyl(PVC) trim. It's not terribly hard to find now and it avoids the need for trying to prevent water intrusion here. Just do some basic caulk for aesthetics and it should be fine.