She may do either from an immigration standpoint, because an E-2 spouse is employment-authorized incident to status once admitted with the spousal notation. Office work can begin at once; hospital nursing requires a state nursing licence, which her status does not provide.
Status gives permission to work; the profession sets its own gate
The spouse of an E-2 investor is admitted in E-2 dependant status and, under current policy, is authorized to work incident to that status without a separate employment document, provided her admission record identifies her as a spouse rather than a child. She may work for the drilling company, for an unrelated employer or for herself. For an administrative role in the company's office nothing further is needed, though her salary should be treated as ordinary payroll rather than as part of the investment.
For nursing, the state board licenses practice independently, and she must satisfy that board's examination and credential requirements before clinical work. Unmarried children under 21 hold dependant status, may attend school and may not work, and each loses eligibility at 21 or on marriage. Every E-2 principal and dependant, including a Canadian citizen, must obtain the appropriate E visa before seeking admission; the wife applies for an E-2 dependant visa regardless of whether she is Canadian.