I have to say I think about nothing all the time, both in the sense of not thinking about anything, and in the sense of contemplating the concept nothing. P.L. Heath has a very fine piece on "Nothing" in the Encyclopedia of Philosophy.
On the other hand I suspect that śūnyatā is not really emptiness or literally nothing - śūnyatā is a kind of non-substantiality, certainly, but in Western metaphysics that does not mean a non-entity. The point is that śūnyatā is emptiness, but of the detritus of external influence, or void or outside dependence. It has its own quality. It is also like a kind of expectant fulness, empty as the rich expectation of a joyous future event is in an obvious sense empty (of the event) compared with the experience of the event itself. A quality however is an entity, though not a substance.