Yes, submit your change of address immediately. Although it may not have any consequences, technically you have violated immigration regulations. But have no fear, they will probably just look the other way.
Yes, better to submit it late then not at all. Moreover, the I-751 requires that you disclose all addresses where you have resided since becoming a lawful permanent resident. Consult with an experienced immigration attorney for case specific advice.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.