Doubt & Answer Explanation

Yes, the dipole will undergo harmonic motion when displaced from its original position of theta = 180^o.

Initially, the dipole will rotate in the same direction in which it is displaced (that is initially there will be no restoring force). So - if we displace +q upwards, then +q will continue to be displaced upwards and the dipole will rotate in the clockwise direction until the +q charge is on the right and the -q charge is on the left. At this point, the dipole will have a certain angular velocity and it will make an angle 0^o with the electric field.

Now the dipole will behave in the same way as it behaves when it is oriented at an angle zero with the electric field and it is slightly displaced downwards.

Now, the dipole will undergo oscillations about its initial position. These oscillations will not however be simple harmonic. Try figuring out how this will happen yourself. Try to draw a diagram and understand exactly what is happening. If you have any problem, post here again and I will tell you exactly what you are confused about.