Married 1/2009 was unaware of husbands past child support issues. Bills all lie on me, too much can I have marriage annulled ?

Your post doesn't contain any legal grounds for annulment. You can file a divorce to end the marriage if you wish to do so.

Time of marriage doesn't really address the issues related to annulment. An annulment is available if there is something that makes the marriage void from its inception. Grounds include fraud in the inducement to marriage, or inability of one of the parties to contract (due to non-age, prior existing marriage, improper relationship, incompetence, etc.) Without knowing more, I cannot say whether annulment is available to you.

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