I'm looking to see if there's an equivalent to the (Property and Contracts) Act 1970 of New South Wales in the US, specifically the part pertaining to minors.
In New South Wales, the common law about minors has been replaced by the Minors (Property and Contracts) Act 1970 (NSW) (the Act) which reduced the age of contractual capacity from 21 to 18 years and described “children” as “minors”.
This isn't done comprehensively in any U.S. state. Instead, it is done mostly piecemeal. Some of the more important laws in Massachusetts are:
In Massachusetts, the age of majority is eighteen. (Massachusetts General Laws Chapter 231, section 85P)
In most circumstances, a contract will be invalid if one party to the contract is a minor. Massachusetts recognizes a few exceptions for necessaries and education, motor vehicle liability insurance (if age sixteen or older), and life insurance (for age 15 or older). (Massachusetts General Laws Chapter 175 sections 113K and 128 and court decisions).
A minor may file a lawsuit against another party though a “next friend,” representative, or guardian ad litem (Rules of Civil Procedure 17(b)).
Other state statutes govern the voting age, tobacco purchasing age, the age at which one can work at particular kinds of jobs, consent to medical treatment, the age of consent for purposes of statutory rape laws (which are generally below age eighteen), the ages for which marriage is possible (without parental or court consent, with court consent, and with parental consent), status as a child for purposes of child support and custody cases, status as a child for purposes of tolling statutes of limitations during minority, statutes of limitations in paternity cases, and ages at which school attendance is mandatory.
Federal law sets an age limit of eighteen years old to act in pornographic material and for moving someone across state lines for the purpose of having sex with them, even though the age of consent in a non-commercial, private context is lower.
Also, for some purposes, an eighteen year old is not an adult. For example, drinking alcohol, buying state law authorized marijuana, service in some elective offices, serving as a fiduciary in a probate estate, guardianship or conservatorship, serving as an officer or director in certain kinds of entities, termination by operation of law of statutory custodianships for minors, etc.