Canonisation of boolean matrices under row and column permutations
This problem is precisely the canonization problem for isomorphism of bipartite undirected graphs. While the lexicographically maximum form may be harder, any canonical form will be GI-hard (and so, in particular, it doesn't matter whether the $P$ and $Q$ are restricted to satisfy $P=Q^{-1}$ or not, as asked in a comment above).

In particular, there is a canonization procedure that takes only $2^{\tilde{O}(\sqrt{n})}$ time (much better than $n! \sim 2^{\Theta(n \log n)}$), by Babai-Luks 1983, though in practice I'd recommend just using nauty.