If a person is able to do Hajj and meets all the conditions of it being obligatory, then he must do Hajj straight away, and it is not permissible for him to delay it.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni:
If a person is obliged to do Hajj and is able to do it, he must do it straight away and it is not permissible for him to delay it. This is the view of Abu Haneefah and Maalik. Allaah says (interpretation of the meaning):
“And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence); and whoever disbelieves [i.e. denies Hajj (pilgrimage to Makkah), then he is a disbeliever of Allaah], then Allaah stands not in need of any of the ‘Aalameen (mankind, jinn and all that exists)”
[Aal ‘Imraan 3:97]
And it was narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever wants to do Hajj, let him hasten to do it.” Narrated by Imam Ahmad, Abu Dawood and Ibn Maajah. According to a version narrated by Ahmad and Ibn Maajah: “…for he may fall sick or be faced with some need.” Classed as hasan by al-Albaani in Saheeh Ibn Maajah. End quote.
What is meant by “let him hasten to do it” is that a person who is accountable must do what is enjoined upon him as soon as he becomes able to do it, and it is not permissible for him to delay it with no excuse.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: Does the command to do Hajj mean that it must be done immediately or may one do it at one's leisure?
The correct view is that it must be done straight away and it is not permissible for a person who is able to go on Hajj to the Sacred House of Allaah to delay it. The same applies to all the duties enjoined by sharee’ah: if there is no set time or reason, they must be done immediately. End quote.
Fataawa Ibn ‘Uthaymeen, 21/13.