The licking cement or eating litter can be an early warning sign - and cats are great at hiding the signs of illness anyway - so it's best get to a vet. We didn't know this, and our kitty was eating litter. In fact, our vet said it often doesn't mean anything. Well, he was wrong. Our kitty was severely anemic by the time there were changes in his playing and behavior. Our vet sent us to a specialist - and when we described the symptoms, the first thing we said was, "he's been eating litter," and the first thing the specialist said to us is "is your cat anemic?" So now our regular vet knows (in fact, he's pretty much an expert now on feline anemia its causes and treatments!). He has a rare disease - but we waited too long - and by the time Tuxie wasn't playing much, it was close. It took two years to fix, it was very expensive, and we almost lost him twice.
Spray the crate with some Feliway. Be as calm as you can be. Place the carrier on the seat, put a seatbelt around it, and open at least one window at least a crack (depending upon how cold it is outside). Talk to kitty the whole way there - tell her she's SUCH a good girl and you know she's unhappy about this, but she needs to see the doctor.
Give her lots of treats when she gets home!