Is it permissible, Islamically, for a girl to travel with her mother only for a one-month training course in a neighboring Arab country, in the event that her father and brothers are unable to travel with them?

A Muslim woman is not permitted to travel without her husband or a [mahram] (a male relative she cannot marry). One woman cannot be a [mahram] for another. Those who permit a woman to travel with companions stipulate that the companions must be trustworthy and the journey obligatory. A mother traveling with her daughter does not constitute a trustworthy companionship. Therefore, she is not permitted to travel except with a [mahram], and she must fear Allah concerning herself during travel and residence.