The month of Dhu’l-Qa`dah (Zilqad) is the first of the Sacred Months to which Almighty Allah has referred in the Holy Qur'¡n. Sayyid Ibn Tawoos defines this month as the month of responding to the prayers in hardships.
It is narrated from the Holy Prophet (Peace be upon him and his progeny) that it is recommended to offer this salaat on Sunday in the month of Dhil Qa'da .Reference to this salaat: Mafateeh Al Jinan by Shiekh Abbas Qummi (page 247),

Benefits in narrations:-

Sins will be forgiven and repentance will be accepted.

Allah (swt) will make liabilities to others cleared and when will die with faith (Iman).

Religion will be intact. Grave will be widened and enlightened.

Parents will be pleased and Allah (swt) will forgive parents and children and will give more wealth.

The Angel of Death will be gentle when taking the soul.

A'maal the month of Dhil Qa'da It is recommended to do Ghusl & Wudhoo ( only Ghusl is insufficient)

Recite a 4 rakat ( 2 X 2) Salaat on any /all Sunday's in Zilqaad month. at any time during the day.

In every Unit/Rakat recite : 
Sura Fatiha/Al Hamd x 1
Sura Ikhlass x 3 
Sura Falaq x 1
Sura Naas x 1  

After Salaam 70 times Istigfaar saying,

I seek the forgiveness of Allah and I repent before Him.

astaghfiru allaha wa atubu ilayhi

أَسْتَغْفِرُ اللّهَ وَأَتُوبُ إلَيْهِ.

                                                Then once

لاَ حَوْلَ وَلاَ قُوَّةَ إِلاَّ بِٱللَّهِ ٱلْعَليِّ ٱلْعَظِيمِ

la hawla wala quwwata illa billahil aliyy'al azeem

There is no power and no strength except with Allah, the Most High, the All-great.

                                                Then once

يَا عَزِيزُ يَا غَفَّارُ

ٱغْفِرْ لِي ذُنُوبِي وَذُنُوبَ جَمِيعِ ٱلْمُؤْمِنِينَ وَٱلْمُؤمِنَاتِ

فَإِنَّهُ لاَ يَغْفِرُ ٱلذُّنُوبَ إِلاَّ انْتَ

Ya azeezu ya ghaffar

ighfir le dhunubi wa dhunuba jameea al mumeneena wal mumnenaati


Fa inna hu la yaghfiru aldhunuba illa anta

O Almighty! O All-forgiving!

(Please) forgive my sins and the sins of all believing men and women,


for none can forgive sins save You.

 so based on the hadith above, can I just do wudu and preform the prayer, or is it wajib to do ghusl for this prayer?


Ghusl is not wajib
Just wudhu is enough.