The first one is correct. The second is not really correct. Better than both would be: "We must hurry. The plane is leaving in an hour and a half".

The difference is that one is natural English and the other is not! The first is a natural comment. In spoken English, it is normal to use the present continuous to refer to a planned or schedule event in the near future. The second is completely unnatural, because 'is to' + [infinitive]' is a very formal construction. You might come across it in written texts, such as a news reports, business letters, contracts and so on. On rare occasions, you might use this in formal spoken language. A native speaker would never use this construction in conversational English.

"the plane is to fly" doesn't make sense to me, but it is a very formal way of saying "the plane is/will take off"