It might be tempting, but do not transport your cat open in the car. Apart from it being really dangerous (kitty can get into your pedal area), it is illegal and the police can fine you. The same applies for going to the vet. Keep her comfortable and safe in a carrier!
Bigger is not better. A cat feels safest when she can brace herself against the sides of a carrier, which is not possible if it is too large. Therefore medium size is the appropriate size for almost all cats. A top-
If your kitty is still growing, it is sufficient to get a washing basket with lid that closes from the top in the beginning (from the supermarkets like LULU, CARREFOUR).
Be aware that for travel in a plane you need a special carrier approved for this kind of purpose!
When the carrier is only used for visits to the vet, the cat might develop a negative behaviour towards the carrier. Leave the carrier out in the room where your cat spends time. By placing a comfortable pillow, blanket or folded up towel, a small catnip toy and a favourite food treat inside you make the carrier a normal part of your cats life. Make sure the door is propped open and that the carrier is backed up against a wall so that there is no chance it will tip over if the cat gets inside and shifts around in there.
Once in a while close the door on the carrier and leave the room for a quarter of an hour. Then come back and open the door, propping it open so the cat has the sense that she can come and go at will. Another time, close the door after the cat goes in, pick up the carrier, and walk it around for a bit. Then set it down, open the door, and offer the cat a treat. On a different occasion you can take the carrier for a drive in the car, even just around the block, and when your return home, set the carrier down, open the door, and offer a special treat.
If the cat just doesn’t get used to the carrier, get a thick towel and wrap it around your cat, making sure her feet are well wrapped so she can’t try to claw her way out. Put her in the carrier all wrapped up and close the door quickly. Don’t worry about the towel – she will unwrap herself inside the carrier.
If the cat does a runner seeing the towel, sit down, talk to her in a calm voice and wait that she comes to you. Then stroke her back while keep talking to her in a soothing voice. Then calmly but firmly scruff her (grabbing the skin fold in the neck – like mother cats do grab her babies). She will roll into the carrying position. Support her butt with the other hand and swiftly manoeuvre her into the carrier. If you are experienced enough you can do it from the front. If you expect immediate resistance, put the carrier on his back with the opening pointing to the ceiling. This way you can lower the cat from the top into the carrier, closing the door on it while it has to jump upwards to get out.