The Householder QR algorithm (used by the qr function) does not compute or store the Q matrix explicitly — it uses an implicit representation of Q in terms of a sequence of elementary reflectors. (In most applications, you don’t need Q explicitly, only a way to multiply any given vector or matrix by Q or Q^*.)
You could implement modified Gram–Schmidt yourself, of course, as @cgeoga suggested, but there is some numerical loss of orthogonality that might bite you unless you use it carefully.
What are you trying to do? What do you need Q for?