Having read so many reviews here on Cruise Critic, I'm well overdue to give back and contribute one of my own.
We took the Diamond Princess from LA to the Mexican Riviera. We were a group of 5, including my wife, a 16-month toddler and my parents.
Travelling to LA was pretty ho-hum. Being from the San Francisco area, we took a flight the morning of the cruise and arrived at noon. We flew into Long Beach airport on JetBlue. Long Beach is nicer because there are less crowds. The thing to remember when bringing things for baby are to declare all liquid items at the TSA table before going to the security checklines. Otherwise, it's either throw-it-out or back to the end of the line. Also, it was our first time having a "lap infant", i.e. not buying a ticket for the kid. We got turned back to the ticket counter because he wasn't listed on the boarding pass at first.