TL;DR: Small changes in the BLAS library will effect the order of operations, so there is no guarantee of identical results between minor Julia versions here.
Although your input matrix is exactly rank deficient, after a few manipulations it is perturbed, so we arrive at
By forming A'A, you make the situation worse (an almost-dependent vector could be obscured). Much more robust would be
F=qrfact(A,Val{true})
ipermute!(abs.(diag(F[:R])) .> eps(10*size(A,1)*F[:R][1,1]), F[:p])
(The 10 is a fairly conservative tolerance factor.) Even this will fail in unusual cases, so you should check the effective rank with an SVD to be safe.