I am thinking about moving out of the state of New Jersey. I have joint legal custody. Can I legally move? If so, what reasons are legitimate or do I need a reason? Do I need permission from a court or the custodial parent as the non custodial parent. Second, will I loose my parental rights by moving?

Legally you can move. However, it may jeopardize your current joint legal custody arrangement. Also the onus of arranging and paying for visitation will fall on you as the parent who voluntarily left the state of residence.

s_cianci's answer is not correct... If you do not have court order or written permission you will lose your rights because it will be treaten as KIDNAPPING
For more information about the law and reasons visit
http://gv70.files.wordpress.com/2007/07/child-relocation.doc
http://gv70.files.wordpress.com/2007/07/relocation.pdf

But she's the non-custodial parent and I don't believe she said or implied anything about taking the child with her.

Yes-If she moves alone-no one can force visitation... but if she takes the child/ren/ with her-it will be awful