2 of 6 Corrected code for antidiagonal.

Octave, 57 70 67 bytes

@(A)all([(s=@sum)(A) s(A,2)' s((d=@spdiags)(A)) s(d(rot90(A)))]==1)

Takes input as a binary matrix with 1 representing a Queen and 0 representing an empty space.

Sample run on ideone.