Your bigger problem will be getting into Canada in the first place. You can't enter Canada (or virtually any other country other than your own) with an expired passport.
According to the U.S. Department of State, U.S. citizens must have a passport that is valid at the time of entry to enter Canada.
That said, Nate's answer is correct. You need your passport to use the Global Entry kiosks at an airport.
According to CBP's Global Entry FAQ (emphasis mine):
How are Global Entry cards used?
CBP accepts Global Entry cards for lawful U.S. entry at land and sea ports of entry. Global Entry cards have radio frequency identification, which enables their use at SENTRI and NEXUS expedited travel lanes entering the U.S. Global Entry cards are not valid for entry into Canada via the NEXUS lanes and kiosks. Global Entry cards are not accepted at Global Entry kiosks, which require passports or U.S. lawful permanent resident cards. Global Entry card holders must follow all program rules for SENTRI and NEXUS when using this card at land and sea ports of entry.
Your best course of action is to try to get your daughter's passport renewed ASAP. According to the Department of State, being within 2 weeks of travel, you should schedule an appointment with a passport agency immediately.