No you don't need to fill out any forms now, you can deal with this next year. However you will want to keep in mind that your taxes will not be taken from your checks automatically. So you will likely end up owning money next year.
While you are not required to fill this out you may want to look at it and consider it. It's a quarterly payment form. Similar to how money is taken out of standard employments checks. The difference is you pay it in manually.
https://www.irs.gov/pub/irs-pdf/f1040es.pdf
