You should consider home insurance for your new home during construction. If you don't, you may be exposing yourself to a great deal of risk if a fire, theft, or other event damages or destroys your partially-completed home.
One way to cover your new home during construction is by purchasing a standard homeowners insurance policy. This will cover you for any damage to the building as it's being built, and may also provide some coverage for theft of building supplies (although the contractor's insurance should also cover this). It also provides liability coverage, which may come in handy if one of your friends trips during a "tour" of your dream house and decides to sue you. However, the policy will not cover your personal property until the building is secure or "lockable." Once construction reaches this point, you can add on homeowners insurance coverage for your personal property.
Another option is to purchase a "dwelling and fire" policy. This type of policy covers damage to the physical structure, but provides no theft coverage. A dwelling and fire policy may be an appropriate choice if you are living in your old house during construction, because the homeowners policy on that house would cover theft of items from the construction site. Dwelling and fire policies also provide liability coverage, just like a standard homeowners policy.
Once the building is complete, you should re-evaluate your coverage. If you opted for dwelling and fire coverage, you may need to purchase a full homeowners policy. If you bought standard homeowners insurance, make sure you have purchased the right amount of insurance, especially if you have made alterations to the original building plans (e.g., adding on a room or upgrading building supplies).