Is it permissible for a girl to marry a committed, bearded man without the permission of her father, who rejects his commitment, provided that her brother acts as her guardian?

The presence of a guardian (wali) is a condition for the validity of marriage. The father is the complete guardian, with whom no one else has guardianship. No one else deserves guardianship except in his absence. If the father refuses to marry his daughter to a suitable match (kufu'), he is considered to be "hindering" (a'dil), and his guardianship falls away and transfers to the next in line among the guardians, or to the judge. Therefore, if the father refuses to marry his daughter to a suitable match, and her brother is an adult, sane, and mature, then he is qualified for guardianship.