Sadly, never assume. My issue with rental car supplied seats is safety (has it been in an accident, where is it stored, has it been dropped, was it recalled, it is expired) and then honestly, cleanliness. Yuck. (because who's kid hasn't soiled the car seat :P)
We use our regular seat for travel - a Diono Radian - as it fits well on planes. So you wouldn't have to buy an additional seat just for travel. I also have a GoGo Babyz cart (after an unsuccessful attempt at using a standard luggage cart, which bent on first use and was much heavier) and LOVE it.
Good luck!
