Car seat regulations vary from country to country. You should always check the road safety rules in effect in your country of residence or the one you are visiting. Your child's safety is at stake.
In Iceland , any child under 135 cm must be placed in a suitable seat..
If your seat meets this standard, bring it along! It's free on the plane and your child will be comfortable, just like at home.
Otherwise, you should consider renting a child seat with your Iceland car rental. This option is payable in advance or at the counter, depending on the rental company.
Please note that not all car rental companies have this option available.