This is going to be a lot of work to DIY and have it be 100% again. A decent size area will need to be sanded (AT LEAST a 6" radius around it), the gouge filled, primered, base coat, and cleared. As each layer goes on, the area to be covered gets larger.
You can buy canned versions of all of the products you will need (primer, base, and clear) but they are expensive ($20-30 per can) and are not as good as their catalyzed counterparts with regards to resilience. You will need sanding block(s) and various high quality wet sand papers. You will also need a filler suitable for use on plastics. A can of silicone remover isn't a bad idea either. The cost is really going to add up. And the result may be that there is more or less metal flake, the flake is a different size, and/or the color is off and the repair is noticeable.
I've done quite a bit of at home DIY 2-stage paint work and it is labor intensive and expensive (lips and diffusers and such). I've had some experience fixing defects in my paint work as well as OEM jobs also. IMO, pay a pro $100 more than you'll spend gathering the supplies and save yourself the trouble. Your other option would be to touch it up and live with it (this is what I would do).
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