Hiya, Diana! Thanks for bringing your question to planDisney!
I am so excited that you will be visiting the Disneyland Resort for the first time! Don't forget to stop by a Guest Relations location to pick up complimentary "First Visit" buttons for the whole family! You are correct that your little one does not require a ticket because they are under 3 years old. They also don't require any sort of documentation to enter the parks. A Cast Member may ask how old they are, but nothing further is needed!
Keep in mind that if you plan to make any
dining reservations, you will want to include your 2-year-old in your party. This will ensure that you are seated at a table that will accommodate your little one in a chair or a high chair if you need it.
Finally, be sure to check out the
Rider Switch service if you want to ride any attractions for which your little one doesn't meet the height requirement. Rider Switch allows one adult to wait with the child outside the attraction while the rest of the party rides. Then after the first party is done riding, the waiting adult and up to two others can then ride the attraction with minimal wait.
I hope your visit to the Happiest Place on Earth is full of magic and memories!
-Linda