No, you do not need a ticket or a theme park reservation for a child who is 2 years old. At the Disneyland Resort, children under the age of 3 are considered "Guests of Mickey" and are admitted for free. They do not require an admission ticket, and because they don't have a ticket, they do not need to be included in the Theme Park Reservation system. You simply bring them with you to the turnstiles. Once a child reaches their 3rd birthday, however, they are required to have both a valid child-rate ticket and a corresponding reservation for every day of their visit. If your child is close to 3, it is helpful (though rarely required) to have a digital copy of their birth certificate on your phone just in case there is a question about their age at the entrance.