don't have vs. haven't got
Today I have written a letter (an exercise is letter writing) and after I asked my sister who has the same English level check it.
She checked my letter and said that "I don't have smth" sounds pretty strange for her. She insisted stubbornly on rewrite "don't have" to "haven't got" because it sounds more natural. I disagreed with her. I think they have the same meaning. Eventually, we didn't reach a consensus.
Do they have the same meaning? Maybe "haven't got" sounds more informal than "don't have".
Thank in advance.
Please, correct all my mistakes. I should know English perfectly and if you show me my mistakes I will achieve my dream a little bit faster. A lot of thanks.