domestic violence

No, complaint under provisions of PDVAct can be filed without lodging FIR.

Hello mam, greetings of the day.
As per your query, No it is not important to file a FIR to file a case of domestic violence in court. You can directly go to the Magistrate to file your case as well.  You can exercise the power of the Protection of Women from Domestic Violence Act, 2005 if you are a victim of domestic violence. 
You can follow the following steps to lodge a complaint.
File a FIR- Incase you are being a victim of domestic violence, you can go to your nearest police station and file a FIR. The police officer will note down your incident. Check thoroughly before signing it. 
Online FIR- You can also file an online FIR if your state provides facilities for the same. You can also file your complaint by visiting the National Commission for Women website.
Directly under a Magistrate- The Magistrate upon receiving your complaint, must commence the hearing of the case within 3 days of the complaint being filed. He will also give the notice for the date of hearing to the Protection officer who shall issue it to the accused. The court after conducting the hearings of the case, and give the judgement as per the evidences present
Hope this helps you.
Regards    
Nirali Nayak
Law Student