When used like this, what acts as a placeholder, analogous to a blank space if the question had been written out, e.g.
Published in 1936, the first issue of Life magazine had a Margaret Bourke-White photo of a _______ on its cover?
The respondent is expected to answer by filling in the blank. Since the article is required when the blank is filled in, it's also used with the placeholder.
But it would also be fine to write it without the article, or to completely invert the question, e.g.
What was the Margaret Bourke-White photo on the cover of the first issue of Life Magazine, published in 1936, a picture of?
These are mainly stylistic choices.