Quarterly Payments Required?

Hi there,

 

This is my first year as an IC (part time) for a company in addition to being employed full time. My IC job is hourly and I expect to earn somewhere around $13,000 for the year (I'm not certain what the total will be since my hours fluctuate week to week but this is a good guess). Will I owe at least $1000 based on these gross earnings and thus need to start quarterly payments? I have not done so up to this point since I would be right on the cusp...but would start tomorrow if necessary. Is there any penalty to overpaying on the IRS website since I don't have previous years to compare to?