Yes, you are correct--you will need a car seat for your child for anything other than the Disneyland Express.
I'm hopping on my soap-box here. Sorry!
As a former car seat tech, I have to mention Best Practices versus the law.... The CA law itself is that any child under 8yo or 4'9" needs to be in a proper child restraint (infant seat, convertible, combination, or booster seat). There's no "in a taxi" exclusion, or "in a passenger van" exclusion that I've seen or heard. Now, best practices would say take a car seat to be used on the plane as well, and then if you need it once off the plane, you are ready to go.
As others have pointed out, some shuttles may provide car seats, but you have no idea what they will be providing--a car seat that was in an accident that wasn't reported? a car seat that's expired? a car seat reeking of baby puke? a plain, unclean, "nasty" car seat? a forward-facing-only seat for a child who is still rear-facing?
I allowed my 7-to-turn-8-year-old-on-our-trip to ride on the plane and on the D-land Express without a car seat. (She's still in a booster--even occasionally harnessed depending on some variables--at home.) I did this because (1) the D-land Express is so big that we would do more damage than anyone could do to us, vehicle wise, (2) the seats are "compartmentalized", meaning they are designed to be safer in the event of a crash, (3) I knew we wouldn't need to go anywhere by car.
Disclaimer: I realize I'm hard-core about this. I'm not trying to offend anyone. I lost multiple family members in a crash where kids were not properly restrained in an SUV, and it's been a cause of mine ever since.