Is she a taxi driver?

Literal

She [topic-は] taxi [genitive-の] driver is [question-か]?

Plain noun-predicate question: [topic]+は+[noun]+ですか. The most common sentence shape for asking about identity, occupation, or attribute. タクシーの運転手 stacks two nouns with の — 'taxi-driver' (literally 'driver of a taxi'). Note that 運転手 is gender-neutral; if the speaker wanted to mark gender, they'd typically use a separate descriptor. Taxi driving in Japan is a notable late-career occupation, often taken up after retirement from another job, and the field has historically skewed older and more male — though this has been slowly shifting.