this might qualify as a sporadic activity provided you did no further work in the IT field. there is no bright line for determining when an activity is sporadic for SE tax purposes. if you so treat it. it is not a business and does not qualify for QBI.
if you treat it as schedule C income then as far as QBI
there is an IRS regulation 1.199A-5(d) that deals with a former employee doing work as an independent contractor within 3 years for the same company. That would make the compensation not eligible for QBI deduction. This can be rebutted.
there is an example in this reg of a lawyer being laid off from law firm A and goes to work for law firm B which provides services to law firm A. this lawyer is involved with providing these services to law firm A. the IRS says that the lawyer's previous work for law firm A disqualifies him from taking the QBI deduction.
there are a similarities in this example to your situation
lawyer laid off
lawyer providing same services as when working for A
(3) Presumption that former employees are still employees—(i) Presumption. Solely for purposes of section 199A(d)(1)(B) and paragraph (d)(1) of this section, an individual that was properly treated as an employee for Federal employment tax purposes by the person to which he or she provided services and who is subsequently treated as other than an employee by such person with regard to the provision of substantially the same services directly or indirectly to the person (or a related person), is presumed, for three years after ceasing to be treated as an employee for Federal employment tax purposes, to be in the trade or business of performing services as an employee with regard to such services. As provided in paragraph (d)(3)(ii) of this section, this presumption may be rebutted upon a showing by the individual that, under Federal tax law, regulations, and principles (including common-law employee classification rules), the individual is performing services in a capacity other than as an employee. This presumption applies regardless of whether the individual provides services directly or indirectly through an entity or entities.
(ii) Rebuttal of presumption. Upon notice from the IRS, an individual rebuts the presumption in paragraph (d)(3)(i) of this section by providing records, such as contracts or partnership agreements, that provide sufficient evidence to corroborate the individual's status as a non-employee.