Hi,
There are several insurers who specialise in the younger market. You could do much worse than to check out (
http://www.performancedirect.co.uk ) or give them a call. Also (
http://www.17to40.co.uk/ ) is worth a look for a quote and advice. Almost lastly try (
http://www.swiftcover.com and
http://www.comparethemarket.com ) as they will give you a huge range of insurers. Lastly look at its's4me insurance too as they are also specialists (
http://www.its4me.co.uk/young-driver-car-insur ance.asp ) If the Ka is not so new then 3rd party fire and theft is a good option to keep price down, and definitely register a SECOND driver on the same car with lots of driving experience too. Normally mom would be best. Don't be tempted to register your daughter as a secondary driver if she is the main driver as many other parents do, this could lead to a criminal conviction should you make a claim and the insurer thinks you have done this. Also your daughter will then benefit by gaining a no claims bonus history of her own if registered as the main driver of her car. If possible keep the declared mileage as low as possible, but true as this will reduce your premium and park it on a drive too if you can.
I hope that this helps