The correct option is
B must not be brought
A notice on the hotel wall usually communicates the instructions/ rules which are to be followed inside the hotel premises. Of the given options, option B is correct, as the auxiliary, 'must' is used to express a rule or an obligation expressed by the speaker (hotel management in this case).
The auxiliary, 'will' is used to express a volition or a choice intended to be exercised. Eg: I will not bring my dog into the hotel room.
The auxiliary, 'have' is used to form the perfect tenses. Eg: 'I have been taking my dog for a walk every evening'. It is also used to express an obligation which comes from somewhere else (i.e not from the speaker). Eg: 'I have to or don't have to) take my dog for a walk every day'.
The sentences: 'Dogs will not be brought into the hotel rooms'; 'Dogs have not been brought into the hotel rooms' and 'Don't do not have to be brought into the hotel rooms' are grammatically correct. However, given their meanings as above, they do not communicate a rule to be followed (which is communicated by a notice on the hotel wall). Hence, options A, C and D are incorrect.