  The scaling behaviour of euclidean quantum gravity at an asymptotically safe
critical point is studied by means of the exact renormalisation group. Gauge
independence is ensured via a specific parameterisation of metric fluctuations
introduced in a recent paper. Within a non-perturbative approximation the beta
function for Newton's constant takes a simple form to all orders in $\hbar$. A
UV fixed point is found to exist for $d\leq 7$ spacetime dimensions at which
the critical scaling can be assessed. The critical exponent for the Newton's
constant $\nu$ is found to be regulator independent close to two dimensions.
Applying Litim's optimisation criteria we find $\nu \approx 1/3$ in four
spacetime dimensions. This value is in agreement with lattice studies
supporting the existence of a second order phase transition between strongly
and weakly coupled phases.
