From RNAfold documentation:

"It also produces PostScript files with plots of the resulting secondary structure graph and a "dot plot" of the base pairing matrix. The dot plot shows a matrix of squares with area proportional to the pairing probability in the upper right half, and one square for each pair in the minimum free energy structure in the lower left half. For each pair i−j with probability p>10E−6 there is a line of the form i j sqrt(p) ubox in the PostScript file, so that the pair probabilities can be easily extracted."

So you could write a script that parses the dot.ps probability matrix and then calculate entropy yourself. An example script for parsing dot.ps file can be found here. Otherwise, I don't think there exists a ready-made solution for your problem