Immediately, and the state licence is the item that governs the calendar. The TN admission itself can be quick for a Canadian citizen with a complete file, but the licence, the employer letter and any I-129 filing each have their own lead time.
The slowest document sets the start date
Four months is realistic for the immigration step and tight for everything around it. Begin with the New York licensing application, because the board's processing time is outside anyone's control and the hospital may refuse to roster her without it. In parallel, ask the employer to draft the TN letter and decide whether the case will be presented at a port of entry or filed on Form I-129; a filed petition adds USCIS processing time, so if the employer prefers that route, the four-month target may need adjusting.
Give notice to the Kingston employer only after the licence status and the TN route are settled, and treat the first shift date as a target rather than an immigration fact. If the household is moving together, add the children's school registration and the husband's plans for his business to the same calendar, since those decisions cannot wait for the last document. Set a document deadline before a travel date, then identify the fact that could stop the move.
Hypothetical example: a Canadian geologist has a field-services offer that begins when spring projects open. His employer letter, degree record, and passport can be assembled promptly, but a required state credential review may govern the start. He must decide whether the firm can assign lawful non-practice duties first or whether the project date should move, rather than appearing for admission with an unresolved work plan.