If he is simply monitoring your social media through use of a fake account, there is nothing the criminal law can do to stop it. Internet or cyber-stalking may be prosecuted under the traditional stalking laws in QLD in some cases, however it requires persistent behaviours that affect you in some way and cause some detriment which may include a well founded fear or apprehension of violence, serious mental, psychological or emotional harm. Simple annoyance does not cut it. If the behaviours escalate to this degree, and you are actually in fear of this man, then I would contact the police or a lawyer about it.
His actions may constitute grounds for private nuisance, however this is a civil action. You would have to prove you have been affected by some act of your ex, that is not trivial or unreasonable. However I doubt the legal expense would be worth it.
Can't you adjust the privacy settings on your social media and de-friend the fake account?
