Is it permissible for me to perform Hajj on behalf of my aunt, who is well-off and in good health, especially since she has married and well-off daughters?

For someone to perform Hajj on behalf of a living person, it is stipulated that the latter must be permanently physically unable to perform it themselves and must grant permission for it. If your aunt is not incapacitated, then it is not permissible to perform Hajj on her behalf, whether it is an obligatory Hajj or a voluntary one. However, the Hanbalis permitted performing Hajj on behalf of a person who is physically able, in the case of a voluntary Hajj. If deputization is permissible, then it is valid whether the proxy is a relative or not, an heir or not.