Disaster Victims Passport and ID Relief Act of 2018 This bill authorizes the President to provide a waiver of document replacement fees to an individual or household in a state that is adversely affected by a major disaster for any of the following: the passport application fee for individuals who lost their U.S. passport, the file search fee for a U.S. passport, the Application for Waiver of Passport and/or Visa form (Form I-193) fee, the Permanent Resident Card replacement form (Form I-90) filing fee, the Declaration of Intention form (Form N-300) filing fee, the Naturalization/Citizenship Document replacement form (Form N-565) filing fee, the Employment Authorization form (Form I-765) filing fee, and the biometric service fee. The bill amends the Robert T. Stafford Disaster Relief and Emergency Assistance Act to include within the definition of "critical services" private nonprofit center-based childcare.