Hi
we took our little man when he was 18 months.
Yes when you hire a car ask for a car seat, it may be a small fee, but most car places have car seats and it will be fitted for you.

Check with Virgin I know that you can carry a certain amount of baby essentials, like stroller without that being classed as your luggage.
as for the theme pasrks, im not sure which one would be the best. our little man just liked watching everything that was going on.