The answer on this question relies upon the specific requirements of each insurance company, so there is no answer that will apply to each situation. We can help with some generalities, please add your experience in the comments to help future visitors.
Most companies do not charge for a person with a learner's permit or require the learner be named on a policy (but some do).
Once your daughter gets her permanent license, she must be covered under your auto insurance, unless she won't be driving. Newly licensed drivers are involved in more accidents than more experienced drivers, so their rates are considerably higher. (See "What a teen does to your car insurance rates")
We'd advise you to notify your car insurance company when anyone in your household gets a learner's permit so that it can let you know when your young driver should be place on the policy.
If your rates really spike up with your teen on your policy, then shop around to make sure you're getting the best rates available.