You need to make the object first, then use []
to set it.
var key = "happyCount";
var obj = {};
obj[key] = someValueArray;
myArray.push(obj);
UPDATE 2021:
Computed property names feature was introduced in ECMAScript 2015 (ES6) that allows you to dynamically compute the names of the object properties in JavaScript object literal notation.
const yourKeyVariable = "happyCount";
const someValueArray= [...];
const obj = {
[yourKeyVariable]: someValueArray,
}