#Octave, <s>57</s> <s>70</s> <s>67</s> 51 bytes

    @(A)all(sum([A A' (d=@spdiags)(A) 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/ksZ3Qv).