I'm pretty sure it'll be over the carry-on limit. It's kind of a tall seat.
You can also keep it sealed in the original box and check it this way. This is usually the only recommended way to transport car seats. The Radian is also steel and less likely to be damaged. The baggage handlers can clearly see that it's a car seat and hopefully wont toss it. The risk of it being 're-routed' are still there but since I assume the cousin doesn't need it at the airport right away, as those of us do who are arriving with our children.
This is how I had my Radian brought to me. My friend was flying with two children and she promised to keep it closed. She was flying alone with two children under stressful circumstances and I was just so grateful to get it over to Europe. My youngest had outgrown her seat and we didn't have a trip to the U.S. planned soon enough.
The box was in good shape when it arrived so I assumed the seat was okay.
Bringing it on board is better, if you can manage it but there is so little space these days, with people trying to avoid baggage charges. Be very careful with it if placed in an overhead bin. It's 25lbs that can come down on someone's head. Push it all the way to the back and try to have it above your own seat. If it's somewhere else, please warn those near by.
You're nice to be willing to do this! So perhaps keep the box, so you can send it down with it inside if you have to gate-check it or the agent says it's too big to bring to the gate.
I once took a car seat on board while working as a Flight Attendant. It was rather amusing for the rest of the crew. I think I stowed it in the crew rest area. "Hey, where's the kid??" It was also funny at Babys-R-Us when they wanted me to drive over and pick it up. I was on a layover. No car. Ummm...you're buying a car seat and you don't have a car?!? Then she gets on the phone "Yeah, this lady's buying a car seat...without a car so you'll have to bring it on to the floor..." Then I told her, I'm here from France and flying to Frankfurt that evening as a working crew member. Then she lightened up, not really sure to believe me...
So hopefully the flight isn't full. Be really nice to all the ground agents and crew and see how far you can get with it! Good luck!