Carrying it
A car seat for a baby or toddler can weigh well over 10 kg. With children, bags and a buggy, it is one more thing to carry through two airports.
In the hold
Airlines usually carry a car seat for a child, but checked seats can be knocked about in the hold, and damage you can’t see may weaken the shell.
Will it be allowed
In Czechia a child seat must be approved to UN R129 or R44/04. A seat approved only to another country’s standard, such as the US one, does not meet that rule.
Renting instead
A rented seat waits for you at arrivals, fits your child’s height and goes back before you fly home. You travel with nothing extra.