Taking your cat to the vets
The vet is your best friend if you're caring for a cat for the very first time. If your cat ever shows any signs of being poorly, don't panic! Make sure you've got your local vet clinic's number handy at all times, along with the opening hours and instructions for after-hours emergencies. If you don't have time to take your cat to the clinic, your vet may be able to advise you over the phone.
You can prepare for all sorts of eventualities before you even leave the house. First of all, if you think she may need an anaesthetic make sure she doesn't eat or drink anything. Secondly, give your vet a call to say you're on the way. This way they can prepare and may be able to save vital time (if your cat's in a really bad way).
On the road
For your cat's (and your own) safety, you'll need a container to put her in while you're travelling. A proper cat carrier is best, but a strong cardboard box will be fine as long as you cut or punch some small holes for ventilation and tie it firmly. Don't make the common mistake of half-filling the box with cushioning – there won't be enough room for your cat! A few layers of newspaper or an old sweater will keep her comfortable.
And remember to stay calm. Soothing words and a familiar toy will help your cat to feel as comfortable as possible.