Is the wife's gold, brought to her at the time of marriage and listed in the prenuptial agreement, considered a debt that must be fulfilled before Hajj, and is the wife's deferred dower (mu'akhkhar) also considered a debt that must be fulfilled before Hajj?

A distinction must be made between the obligation of Hajj and its permissibility. If a person has a debt that prevents him from performing Hajj, or prevents the repayment of the debt if he were to perform Hajj, then Hajj is not obligatory upon him, unless he is reasonably certain that he will find the means to repay his deferred debt when it becomes due. Deferred dower and gold taken from the wife are treated like other debts.