Getting re-married, by itself, will not affect your child-support payments. You may want to consider filing your taxes separately from your new husband to prevent your former spouse from using your new husband's wage information as ammunition for a bogus legal argument.
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.