TurboTax might show your Virginia state tax as $0 even though your taxable income is $600 for a few reasons:
Low Tax Bracket: Virginia's lowest tax rate is 2% if your taxable income under $3,000. Since your income is $600, it's below this threshold, your normal tax would only be about $12.00 - see Table here,
Credits and Deductions: You might qualify for credits or deductions that reduce your tax liability to zero. The lowest Virgnia standard deduction is $8,500.