  In this paper we show how one can obtain simultaneous rational approximants
for $\zeta_q(1)$ and $\zeta_q(2)$ with a common denominator by means of
Hermite-Pade approximation using multiple little q-Jacobi polynomials and we
show that properties of these rational approximants prove that 1, $\zeta_q(1)$,
$\zeta_q(2)$ are linearly independent over the rationals. In particular this
implies that $\zeta_q(1)$ and $\zeta_q(2)$ are irrational. Furthermore we give
an upper bound for the measure of irrationality.
