Your element is not an array, however your cart needs to be an array in order to support many element objects. Code example:
var element = {}, cart = [];
element.id = id;
element.quantity = quantity;
cart.push(element);
If you want cart to be an array of objects in the form { element: { id: 10, quantity: 1} }
then perform:
var element = {}, cart = [];
element.id = id;
element.quantity = quantity;
cart.push({element: element});
JSON.stringify()
was mentioned as a concern in the comment:
>> JSON.stringify([{a: 1}, {a: 2}])
"[{"a":1},{"a":2}]"