Is it permissible for my 22-year-old daughter to travel with me on a business trip due to the absence of family for me?

A woman is not permitted to travel without a mahram (unmarriageable kin) except for the obligatory Hajj and Umrah, provided there is a safe company. If your travel is for a necessity or an urgent need, and you cannot find a mahram, then there is no objection to you traveling with your daughter, provided the journey is safe. Some scholars have even allowed a woman to travel with a safe company for any journey undertaken in obedience to God.