The Quantity selector. It is good that you thought of this and added it to the search bar. But, it becomes complex when a user adds certain quantity of a thing to the basket. And then when they search, we should show them the current quantity. If any change is done to the number, then the button should change to 'Update Basket' or something. Basically, the fact is: it becomes convoluted.
How often does people use this? you have not mentioned particularly about the products listed in your site. So I assume it consits of some which are less expensive and some that are costly. People do not actually buy off something just like that. They need to check the specifications, description, warranty and reviews before buying something. Therefore, a big research needs to be done on 'How often' does one use this.
Size & Colour. Some items have size and colour selectors too. This comes on top of quantity. It cannot be included in this model.
(Bonus Point) From a business point of view: We will not be able to show add-ons of the products that people generally buy together with this. Like: Mobile+Mobile Case+Headset.
Conclusion: This model can be used for basic shops only, where the users are well aware of the 'search-lists/items in the shop'.
A simple alternative would be to add a "Favourite/Add to Wishlist/Buy Later" button.