All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
A woman who has determined to perform Hajj has to know that being accompanied by a Mahram (unmarriageable man) is an essential condition for Hajj. If she travels for Hajj without a Mahram, her Hajj is valid but such a breach constitutes a sin according to the dominant opinion among the Muslim scholars. The Sharee'ah rulings are not changed due to change in means of travel even if they become easy and safe.
For more benefit, so please refer to Fataawa 82195 and 81435.
Know that your father is not allowed to prevent you from performing the obligatory Hajj if it becomes due and obligatory on you. So, it is not your duty to obey your father in such a matter since performing Hajj is an obligation that should be done at once as long as one is able to do so. Such "a disobedience" to your father is not a form of ingratitude.
In this vein, the Prophet said: “There should be no obedience to a human being if such an action constitutes disobedience to The Creator.” [Ahmad and Al-Haakim from Ali. Al-Albaani graded it as sound]
Another Hadeeth reads: “Obedience is required only in what is permissible and reasonable.” [Al-Bukhari]
Such rulings include parents and all people.
Based on the above-stated points, it is your duty to perform Hajj since you are able to do so and there is a Mahram for you (your uncle). So, you are not allowed to travel alone: (1) according to the predominant opinion among Muslim scholars, (2) due to weakness of the opposite opinion, and (3) traveling alone results in many risks that are rejected by the Sharee'ah. In addition, there is no need for your parents' consent. But, it is better to do your best to convince them, since such an action is considered as a good reconciliation between fulfilling an obligation and obtaining the parents' contentment.
Allah knows best.