Answer
Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister, thank you for your question that shows your interest in knowing more about Islam and your zeal to perform Hajj on behalf of your dead parent.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states,
Certainly, you can perform Hajj for your dead parent. However, before you do that, you need to do hajj for yourself first. Also, if your father or mother sets aside some funds before they died for someone to do hajj on their behalf, then you may do it on their behalf using their funds.
The Prophet (peace and blessings be upon him) told a man who was doing hajj on behalf of his brother or relative, called Shubramah, who had never done hajj for himself, “First do hajj for yourself, then you can do it (next year) for Shubramah.” (Abu Dawud from Ibn `Abbas)
Allah Almighty knows best.