Is it permissible for a woman to travel by plane with a group of female teachers without a mahram to work in a Gulf country and reside in a safe accommodation, given that she has a married sister in the same country, and knowing that her financial situation in her home country is good?

It is forbidden for a woman to travel without a mahram. However, her residence in another country does not require the presence of a mahram; rather, it requires that she be safe therein. If a woman is able to travel with a mahram and is safe in the country she travels to, then there is no objection to that. Otherwise, she is not permitted to travel.