You don't need to remit quarterly payments if your other withholding can cover this liability. If you make $300 per week after expenses, that's in the ballpark of $15,000 in net income per year. You must cover the regular tax rate on that income, plus Self-Employment tax. The SE tax would be about $2100 on $15,000 in net income. If your income tax rate is 15%, you can add another $2250 to that. Your tax return can also be impacted by an increase in income, which can reduce certain credits and deductions.
So, does your current withholding cover an additional c $4350 in tax liability? If your refunds are usually low, not paying estimated taxes can cause you to pay a penalty and owe a big chunk when you file.
You don't absolutely have to make the estimated payments. You can see how it goes and prepare to pay when you file. Its just a good idea to make some changes to pay in a little more during the year.
I would recommend that you at least lower your day job's W4 exemptions or add an additional amount per paycheck. For instance, if you are claiming Single 1, change to Single 0 so they can take out more. If claiming 0, maybe add $50 per paycheck. Or do both.
