Adding elements to object

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}]"