I have what looks like brown algae growing on a live plant in my smaller tank. Is this possible, what else could it be? What can one do about this?

It's usually black brush, not brown algae, that grows on the plants. Maybe google black brush algae, and see if that's it.

Brown Algae only grows in low light environments, if you are growing plants then it is not brown algae as the plants need a higher wattage of light than the algae needs to sustain itself. The common plant killer algae is black brush and green algae.