Can the offer and acceptance (ijab and qabul) be said in a state dialect, such as Kelantanese or Terengganu dialect?

Yes, as long as the meaning is clearly a marriage contract and it is understood by the wali, the groom and the witnesses. The validity of the contract depends on the meaning of the words, not on standard language. However, a very thick dialect can make things hard for witnesses or an officiant from outside the district. That is why most officiants use standard wording in Malay. If your father is more comfortable in his dialect, discuss it with the officiant first. Make sure the groom's name, the father's name and the mahr are said clearly. If doubt arises after the contract, consult the marriage officer. See the language of ijab and qabul.