In general, the water flowing through your filter and agitating the water to mix it may provide enough oxygenation. Most of the oxygen absorbed into water is done at the surface; bubbling air through the water actually contributes a fairly low amount to dissolved oxygen, although the bubbles moving the water around might contribute to churning the more oxygen-rich water towards the bottom of the aquarium.
Water temperature (warm water can hold less dissolved gas of all kinds, including O2) and plants (lots of plants/algae with not enough light for photosynthesis) can have an effect on oxygen levels as well.
Absent any reason to think you have low oxygen levels (like your fish congregating around where the filter water is pouring and avoiding the lower parts of the tank), your waterfall is probably sufficient.