  We numerically investigate the generation of a magnetic field in a
protostellar disc via an $\alpha \Omega$-dynamo and the resulting
magnetohydrodynamic (MHD) driven outflows. We find that for small values of the
dimensionless dynamo parameter $\alpha_d$ the poloidal field grows
exponentially at a rate $\sigma \propto \Omega_K \sqrt{\alpha_d}$, before
saturating to a value $\propto \sqrt{\alpha_d}$. The dynamo excites dipole and
octupole modes, but quadrupole modes are suppressed, because of the symmetries
of the seed field. Initial seed fields too weak to launch MHD outflows are
found to grow sufficiently to launch winds with observationally relevant mass
fluxes of order $10^{-9} M_{\odot}/\rm{yr}$ for T Tauri stars. This suggests
$\alpha \Omega$-dynamos may be responsible for generating magnetic fields
strong enough to launch observed outflows.
