"Haven't" is an auxiliary (helping) verb, so you must add another verb. "Haven't got" works perfectly fine for possession. I don't have a dog. I haven't got a dog.

So far I have only heard "I have" and "I haven't" being used in Canadian English - like: Have you any evidence? But "have" is an auxiliary, so you need a verb in the sentence: Do you have any evidence?

Haven't = 'have not' and Don't have = 'do not have' To keep it simple (though it's not always the case), use "don't have" to refer to nouns and "haven't" to refer to verbs/actions. (don't have) E.g: I don't have any paper. I don't have an apple. I don't have any food. (haven't) E.g: I haven't seen her. I haven't gone to school today. I haven't prayed yet. I haven't slept properly. Hope this helps and good luck!!!! :D