Yes, according to this Turbo Tax post, you would report this as Self-Employed income because the company did not withhold federal income, social security or Medicare taxes from your income. As a result, you are responsible for any and all additional taxes you potentially owe.
Since you are responsible for these additional taxes as a self-employed person, you are eligible for QBI. Note, in the post it mentions that you should have been issued a 1099-MISC. This is an older post and the 1099-MISC has been replaced by a 1099-NEC. The tax code however still applies regardless of the tax form that was issued.