There is nothing wrong for you in making a marriage ceremony with a justice of peace for legal purposes if you have already performed the nikah as required by Islam. It is also equally permissible for a Muslim bride to walk down the aisle for this purpose.

Having said this, however, it had been ideal and advisable for you to get everything done in one simple ceremony: combining both religious and legal if you are living in a city where there is a mosque; for generally the imams have the license to solemnize marriage according to the laws of the province; and so he would be able to complete both requirements, religious and legal, in which case no such question would ever arise.