Two Perpendicular Chords

Let $P$ be the bottom vertex of the ellipse $E \colon \dfrac{x^2}{4} + y^2 = 1$. Two mutually perpendicular lines $l_1, l_2$ pass through $P$: the line $l_1$ meets the circle $x^2 + y^2 = 4$ at $A$ and $B$, while $l_2$ meets the ellipse $E$ again at a point $Q \neq P$. Find the range of possible areas of $\triangle QAB$.