You can't do Hajj at ANYTIME except its specified due time in the 12th month of Dhu al-Hijjah.
Umrah, on the other hand, is open ended; you can do it absolutely anytime. The best time for Umrah (the time when the Prophet (PBUH) did all of his 4 Umrahs) is the 11th Arabic month of Dhu al-Qa'dah.
