Why not just do one there? Why bring one along?
On the other hand why not call where you're going to be renting a car and get that out of the way. This way you can make sure you're going to have exactly what is needed.
By asking them about car seat rental you are getting the correct information. They don't want you to be ticketed while using their vehicle and car seat for either one NOT being up to date and correct.
So my point is this. Call and plan your vehicle rental ahead of time, like...now? Ask them about renting a car seat. What car seat do they say your child must use? If they say "Your child is old enough to do just a backless booster and we rent those for $XX.00 for the entire week you'll be here". Then you know which car seat is required. No questions. They should be the experts if they're renting them.
Then you have the option to say "Well, I think we are bringing her car seat with us for when we're in taxi's and stuff so I don't think we'll need that for sure. Can I arrange that the day we arrive if we decide to do that?" then you can see if you want to bring hers or just rent one.
When we've traveled we've learned that car rental places can run out of vehicles during busy times so calling ahead and making rental arrangements isn't a bad idea. They should know what you need.