#Octave, <s>57</s> <s>70</s> 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](https://ideone.com/H30D5A).