I have full custody of my children, ages 16 and 12, and am moving from Portland, OR to Scottsdale, AZ for a job. The children's mother lives in Albany, NY and only sees them 1-2 times each year. This will cause no hardship on her end. What documents must be prepared and filed with the state of Oregon prior to the move!
This depends in some part on the exact contents of your general judgment awarding custody, which should be evaluated in full by an attorney before you do anything.
Usually custody judgments require that if you're going to move (more than 60 miles) you must give the other parent reasonable written notice of the intent move to give her time to contest it by filing for a change of custody if she chooses. Naturally, her presence in upstate New York will make her case rather weaker. But these things are highly individualized, and you should seek professional advice before moving forward with anything - including the move.