We consider the hyperk???????hler extension of Teichm???????ller space with the Weil- Petersson metric. We describe its recent construction as a hyperk???????hler quotient and examine the defining equations for the resulting moduli space. We examine relations between this moduli space and the quasi-Fuchsian deformation space of the surface, with particular attention to the connection with the canonical holomorphic symplectic structure. We also consider the connection with Taubes moduli space of hyperbolic germs and whether it is possible to extend the hyperk???????hler structure in any fashion.