She'll be fine with warm blankets.Bring extra blankets in case of a pee accident.That we do because sometimes they get nervous and pee....but I wouldn't worry too much.Don't open the car door at all if you have to throw in an extra blanket.She could get loose.Always have the cage door shut and locked if the car door is opened for any reason.
In fact don't open the cage door at all unless you know she's soaked and need a new blanket.She sounds like she's in great hands anyway Don't worry...she'll be fine.