Yes. Both are perfectly correct.

First of all thanks for your instant answer, then: You wrote: "She had do go or else she would miss her flight ...", In the above sentence, is "had do go" a mistake or it is inentionally used? I mean "had to go" or "had do go"? Thanks.

check this out : had to in affirmative sentences (Simple Past) Example: I/you/he/she/it/we/you/they had to get up early. had to in negative sentences (Simple Past) Example: I/you/he/she/it/we/you/they did not have to get up early contracted forms: I/you/he/she/it/we/you/they didn't have to get up early. to sum up it seams when you want answer in negative form(no matter whether it's in affirmative or negative sentence) you can say that with did ....

Oops: "to go" not "do go."

An example for both instances could be (to express why "going" was necessary): She had do go or else she would miss her flight, so she went and she made her flight. Or: She had do go or else she would miss her flight, but she didn't go and she missed her flight.