Yes, unless special circumstances arise.
Quoting V C Section 27360,
(a) Except as provided in Section 27363 a parent, legal guardian, or driver shall not transport on a highway in a motor vehicle, as defined in paragraph (1) of subdivision ( ) (c) of Section 27315, a child or ward who is under eight years of age, without properly securing that child in a rear seat in an appropriate child passenger restraint system meeting applicable federal motor vehicle safety standards.
(b) Subdivision (a) does not apply to a driver if the parent or legal guardian of the child is also present in the motor vehicle and is not the driver.
Note that (b) is an important clause in some cases.
The exemptions provided for in V C Section 27363 do not include anything general related to transport to or from airports; most relate only to the regulations that state that children must be in a rear seat. Here are the main ones:
(1) There is no rear seat.
(2) The rear seats are side-facing jump seats.
(3) The rear seats are rear-facing seats.
(4) The child passenger restraint system cannot be installed properly in the rear seat.
(5) All rear seats are already occupied by children seven years of age or under.
(6) Medical reasons necessitate that the child or ward not ride in the rear seat. The court may require satisfactory proof of the child's medical condition.