Answer

By Your Horse

If you’re only accepting some diesel money, this isn’t legally regarded as ‘hire and reward’, and your own vehicle insurance is adequate. Should you charge per trip, you’d need to be covered for commercial hire and reward.
Your friend’s insurance should cover injury and accidental death while in your lorry. If she doesn’t have this cover, you would need to take out a policy called care, custody and control, which covers for injury or accidental death of any horse not belonging to you.