If under 25, the cheapest insurance might be the ones that come with a telematics box that gets installed in the car and tracks their driving. One downside of this approach is if the insurer refuses to cover after the first year, then you have to disclose that to future insurers.
Boxymo was one of the first offering this, but it's available from a few insurers now including
123GO from 123.ie (RSA)
AIG Box clever
Also try the insurer they had named driving experience with as they may offer a discount. If you're insured with Aviva as an example, and your daughter lives at the same address as you, they'll give a multi car discount to you both.
A few insurers will allow a discount for named driving experience, but not all. They don't all allow for it on their online quote forms though so you might have to phone.