In New Jersey, a Court will consult the New Jersey Child Support Guidelines before entering or modifying an award of child support. The Child Support Guidelines were intended to be used in all cases where the parties' combined weekly net income does not exceed $2,900.00.The guidelines are used as a rebuttable presumption of what is the correct amount of support for the children. Therefore, Courts may only deviate from the guidelines upon good cause, where a party (in this case, the mother) shows that circumstances exist that make a guidelines-based award inappropriate. Based on what you have said, it does not appear that there is any reason for the Court to deviate from the guidelines. So if the current child support award is a guidelines-based award, then your child support will not increase. However, there may be more relevant facts than you have provided, and it would be beneficial for you to consult an attorney if you are concerned.
The courts look at combined income in most states and the amount of child support awarded to the custodial parent is regulated by statute. There usually needs to be a material change is circumstances to warrant a change in the amount of support, which Tennessee case law says it needs to be an amount of at least 15%. You should consult with an attorney to make sure your numbers are where they should be and to make sure your rights are represented. The attorney would know how to account for your ex's income as well. And if it's in the child's best interests, you might be able to petition your judge to order an increase in your time with your child.
The following answer is general legal information and is not intended to establish an attorney-client relationship.
She would have to demonstrate that you suggesting that she move is a "change in circumstances" warranting a re-evaluation of support. Then, if she made that hurdle, the court apply the CS guidelines (see the other answers). Can't say if your support would go up, down, or stay the same under those circumstances.
IF YOU LIKE THIS ANSWER AND APPRECIATE THE TIME IT TOOK TO WRITE IT, PLEASE SELECT IT AS "BEST ANSWER." Thanks. The above is said without seeing your case file and without my understanding the entirety of the facts of your case. Depending on those facts, the above information be may incomplete or may be completely inaccurate. The above is intended as general information only based on what you described and not as legal advice. I advise you to consult with counsel who may be able to provide better information commensurate with a better understanding of your situation.
From your facts it does not appear that she will get an increase in child support. You are correct and you could request a temporary transfer in custody for the best interest of the child.