While I do not know for certain off the top of my head what NY state statutes are...
In general most states require that the couple be married for at least one year prior to an adoption taking place to prove a stable household and family.
A smooth, noncontested adoption usually takes 5-6 months from start to finish, providing the courts are not back logged and you can get a quick hearing. Once you are married I would begin getting the documents that are needed, extra marriage certificates, birth certificates for everyone in the household, as these can take some time to aquire as well.
While you may not need to use an attorney for the actual process, you can still make an appointment for a free consultation to get more information from one as to what the actual laws are in the county that you live in ( as adoption laws vary not only from state to state but county to county) so that you will have a better idea as to what it is that you are going to be dealing with.
http://stepparent.adoptionblogs.com/