There are two different kinds of coating you can do: Paint Protection Film (PPF) or ceramic coating. As far as I know, only PPF can be dealer-installed.
PPF protects against rock chips/scratches, and it is usually only applied to the hood, fenders, bumper, and mirrors (though you can also get PPF for the lower portion of the doors to protect against road contaminants). Ceramic coating will not protect against rock chips or scratches, but it provides a hydrophobic effect that makes the car easier to wash and keep clean, and also provides excellent UV protection (same as waxes/sealants, but is advertised to be much more durable). Ceramic coating is usually done on the entire vehicle and can last from 3 years to 8-10 years.
They both vary in professional installation costs, anywhere between $400-800 for either. My advice for a new car would be to have PPF installed, then give the car a proper detail (wash/decontaminate/polish/wax) 1-2x a year. That way, you get rock chip/scratch protection on the front and UV protection on the whole car.
EDIT: In your case, I would suggest getting a touch-up paint pen from Mazda. If the chips are small enough, the paint pen will fill them in easily.