Initially, my thoughts were "work generates a paycheck and is how you earn you living" but, according to webster, that is "employment"
so, yes, babysitting for sure is work!
Main Entry: 1work
Pronunciation: 'w&rk
Function: noun
Etymology: Middle English werk, work, from Old English werc, weorc; akin to Old High German werc work, Greek ergon, Avestan var&zem activity
Date: before 12th century
1 : activity in which one exerts strength or faculties to do or perform something: a : sustained physical or mental effort to overcome obstacles and achieve an objective or result b : the labor, task, or duty that is one's accustomed means of livelihood c : a specific task, duty, function, or assignment often being a part or phase of some larger activity
2 a : energy expended by natural phenomena b : the result of such energy <sand dunes are the work of sea and wind> c : the transference of energy that is produced by the motion of the point of application of a force and is measured by multiplying the force and the displacement of its point of application in the line of action
7 a : something produced or accomplished by effort, exertion, or exercise of skill <this book is the work of many hands> b : something produced by the exercise of creative talent or expenditure of creative effort : artistic production
8 plural : performance of moral or religious acts <salvation by works>
9 a : effective operation : EFFECT, RESULT <wait for time to do its healing work> b : manner of working : WORKMANSHIP, EXECUTION
-synonyms WORK, EMPLOYMENT, OCCUPATION, CALLING, PURSUIT, Métier, BUSINESS mean a specific sustained activity engaged in especially in earning one's living. WORK may apply to any purposeful activity whether remunerative or not <her work as a hospital volunteer>. EMPLOYMENT implies work for which one has been engaged and is being paid by an employer <your employment with this firm is hereby terminated>. OCCUPATION implies work in which one engages regularly especially as a result of training <his occupation as a trained auto mechanic>. CALLING applies to an occupation viewed as a vocation or profession <the ministry seemed my true calling>. PURSUIT suggests a trade, profession, or avocation followed with zeal or steady interest <her family considered medicine the only proper pursuit>. Métier implies a calling or pursuit for which one believes oneself to be especially fitted <acting was my one and only métier>. BUSINESS suggests activity in commerce or the management of money and affairs <the business of managing a hotel>.