Her epistemology is that there is a reality independent of our senses, but which we can best detect through our senses. It does not seem to be a very sophisticated or developed theory of knowledge and certainly does not seem to betray any knowledge of or interaction with the field of epistemology and the many theories of knowledge from ancient to modern times.
Reality as a primary and independent of consciousness is Aristotle's discovery that Ayn Rand took as a foundation of her philosophy. Her own epistemological crowning achievement is her theory of concepts: concepts are objective, i.e. based on reality and formed by a rational method. This is her solution to the "problem of the universals". Check out Rand's "Introduction to Objectivist Epistemology" for details. And, it's only a ~100 pages long.
In between Aristotle and Rand are nearly 2500 years of philosophy, and I don't really see her engaging with any of that.
She chose to not "engage with any of that" because she considered and rejected it as being false. Was she right? You have to read her arguments.
Lack of engagement is a signal that a person doesn't have the intellectual rigor to be taken seriously.
I know little about Rand. Did she engage with Aristotle?
Her notion of "happiness" appears to me to be related to the Aristotelian ideal.
The problem is that 'reality' (i.e. what is actually happening in the universe) is subjective to each of us and that subjectivity is due to the manner in which our senses percieve and our brain filters and prioritizes. Then, on top of that, you have emotions thrown in for good measure. Then, on top of that, you've got our experiences and education (about the world and life) filtering and coloring perceptions even further. Then, on top of that, you've got your reaction to what you thought you saw; again colored by emotions, experiences, and education, and genetics (and epi-genetics). In the end you have to ask "Did I just see what I thought I saw?". The answer is "Yes" and "No".