。
She had her luggage taken to the airport.
Literal
She [topic-は] luggage [object-を] airport [as-far-as-まで] carry-received.
~てもらう is half of Japan's giving-and-receiving (授受) verb system: it marks the speaker (or topic) as the recipient of a favor — V-て + もらう = 'have/get someone to V (for one).' Here she had someone deliver her luggage. The agent is left unspecified — most likely a service worker or driver — but the construction itself signals that she received a service and was the one to benefit. まで marks the endpoint of motion ('all the way to'), shading the journey as longer than just 'to.'