If you add your daughter to your policy as 'named driver' then, fairly obviously, she'll be covered under your insurance policy. (Adding a named driver usually doesn't cost much. Under some circumstances it can actually result in a reduction in the cost of a policy).
Otherwise though your daughter will need to read the fine print in her own policy. At one time all 'fully comp' policies (and quite a few others too) automatically included '3rd party only' cover for driving someone else's car with their permission (subject to certain exclusions, which aren't relevant here anyway). However, in an attempt to cut costs, many insurers decided to remove such cover from their policies, so it's now a case of 'some do and some don't'. [I insure my car through Post Office Insurance, accepting the cheapest deal they can offer. At the moment I'm covered to drive someone else's car but the previous policy I had through Post Office Insurance didn't provide such cover].
Remember that, even if your daughter's policy allows her to drive your car, the cover will be '3rd party only. (So nobody will pay out if she prangs your car). If you add her name to your own policy though then (assuming the policy is 'fully comp') your insurer will pay out if your daughter damages your car.