Praise be to Allah.
I ask Allaah to reward you for your kind feelings towards your mother and your eagerness to perform your filial duty towards her after her death. In response to your question, if a Muslim wishes to perform Hajj on behalf of someone else, he must first have performed it for himself. The daleel (evidence) for that is the hadeeth of Ibn ‘Abbaas, according to which the Prophet (Peace & Blessings of Allaah be upon Him) heard a man saying
“Labbayk (here I am) on behalf of Shubrumah” [i.e., he was performing Hajj on behalf of Shubrumah]. He (the Prophet) asked, “Who is Shubrumah?” The man said: “He is a brother (or a relative) of mine.” He asked, “Have you performed Hajj for yourself?” He said, “No.” He told him: “Perform Hajj for yourself, first, then perform Hajj on behalf of Shubrumah.” (Reported by Abu Dawud in Al-Sunan, Kitaab al-Manaasik, Baab al-rajul yuhijj ‘an ghayrihi).
This is a saheeh hadeeth. I ask Allaah to forgive your mother and extend His Mercy to her, for Allah is the best of Helpers.