No, that is not correct. If your business is a single-member LLC then your business for tax purposes is considered a disregarded entity as the taxes are paid through your personal return. Because you live in Virginia and I assume you conduct your business in Virginia the income from the business is reported on your Virginia return.
If you are a multi-member LLC, then the business is considered a partnership. A Partnership informational return Form 1065 is prepared and the partners will receive a Schedule K-1. Each partner then reports their share of the profits/losses on their individual Form 1040. Thus requiring the reporting of the income on your Virginia State Return.
Simply because you have formed and registered your business in Delaware does not mean it eliminates you from filing a state tax return.
