The work done by an external agent in rotating an electric dipole from an initial angle $\theta_0$ to a final angle $\theta_1$ in a uniform electric field is given by the change in potential energy: $W = U_{\theta_1} - U_{\theta_0} = pE(\cos\theta_0 - \cos\theta_1)$ [NCERT Class 12, Physics Part I, Sec 2.8.3, Eq 2.31].

1. Initial Position: The dipole is lying along the electric field, which corresponds to the position of stable equilibrium. Thus, $\theta_0 = 0^{\circ}$.
2. Final Position: The dipole is rotated by $90^{\circ}$. Thus, $\theta_1 = 90^{\circ}$.
3. Calculation: $W = pE(\cos 0^{\circ} - \cos 90^{\circ})$ $W = pE(1 - 0)$ $W = pE$