I would not recommend a dedicated booster seat for a 3yr old. When you move a child from a 5-pt harness seat to a booster w/adult seatbelt, the responsibility to stay seated properly 100% of the time shifts from the parent to the child. The child cannot lean forward, twist around, slump, put the shoulder belt under their arm, or fall asleep in a booster seat. Most 3yr olds are not mature enough to ride sitting correctly for 100% of the car ride in a booster.
Car rental seats cost about $10 a day and you don't know the history of the seat. Carseats that have ever been in an accident should not be reused. I'd suggest buying one and bring it with you.
This site has a list of recommended car seats with pros and cons:
http://www.carseatsite.com/recommended_car_seats.htm
I'd sit your dd down next to a wall and measure her torso (bum to top of shoulder). The seat needs to have a harness that has top harness slots that are taller than her shoulders (harness needs to be at or above the shoulders in fwd facing mode - if not, it can cause spinal injuries).
Then you can look at this site and it shows you car seat harness measurements:
http://www.carseatdata.org/measurements.php?tun=home
I would recommend a combination seat. The
evenflo Generations or Bolero (less expensive version found at Kmart/
Walmart) has 16.5-17" top harness slots and harnesses to 40lbs, then converts to a decent booster seat. It is airline approved as well.
The
Cosco/Safety 1st Apex harnesses to 65lbs (17" top slots), then converts to a decent booster. I believe it's airline approved as well, but it would be pretty bulky to travel with. It's the
only combination harness to booster seat available that harnesses past 40lbs. Another con: This seat
requires a tall vehicle seatback/headrest behind it.
FAA Child Safety on Airplanes
http://www.faa.gov/passengers/fly_children/crs/
hth