Looking at the style it appears to be a chassis frame with a thin skin over it for cosmetic purposes. The easiest way to build it would be to copy the construction in the model.
If I was making it with card I'd make laminated strips of thick card like mounting board to make the bars that form the chassis frame. I'd glue them together with superglue then also coat the outside with superglue so it sets solid. It's best to do this in a well ventilated room for obvious reasons.
The areas under the hood won't be visible so I'd make the basic form with the thick card and then cover it with a skin from thinner card to make the shape. When making a
three wheeled racing car a while back (for reasons which are not obvious but doubtless seemed valid at the time) I used this approach.
You can see it in this picture where the small former at the back of the car is still visible. You can then cover it with a "skin" of thinner card as with the prototype.
The wheels may be a challenge. Personally I'd make solid discs and paint the "holes" later, although the tyres can be made with thin card rolled around the wheel and superglued as before then filed/sanded to shape: the challenge will be getting them the same shape, especially after inhaling those lovely superglue fumes. You'll probably spend more on superglue than card for the project.
Painting will be fun too...
Hope that helps. Let me know if I've not explained some points very well...
and a couple of lindor thingies.
Especially since what you suggest is more or less how I thought of going about it.
