She can hold L-2 status until her 21st birthday and may study during that time. After 21 she is no longer a dependant and will need her own status, most likely F-1 as a student, applied for before her L-2 ends.
One year of L-2, then her own status
Unmarried children under 21 qualify for L-2, and a university student may enrol in a U.S. institution in L-2 status without a student visa. The difficulty is arithmetic.
On a two-year assignment she will turn 21 during the first year, and L-2 ends on that birthday regardless of the parent's continued status. Before then she must either change to a status of her own or leave. The usual choice is F-1, which requires admission to a school certified for international students, a Form I-20 and a change-of-status application filed with USCIS while she is still in valid L-2; alternatively she can return to Canada and apply for the F-1 visa there.
Either way, plan it from the start, because a change of status filed after the birthday is late. She may not work in L-2; F-1 permits limited on-campus employment. The L-2 spouse, by contrast, is employment-authorized incident to status and may work for any employer.