A Tangent Quadrilateral Locus and Area

Let $P$ be a moving point on the ellipse $C:\dfrac{x^2}3+\dfrac{y^2}2=1$. The two tangent lines from $P$ to the circle $x^2+y^2=1$ meet the ellipse again at points $A$ and $B$; from $A$ and $B$, the other tangent lines $AQ$, $BQ$ to the circle $O$ meet at a point $Q$.

1. Find the equation of the locus of $Q$. 2. Find the range of the area of the quadrilateral $PAQB$ (to four decimal places).