It should... Because 4 doors = sedan = family car and 2 doors = coupe = sports car.
Is it because you have 3rd party+fire+theft? But I'm pretty sure that doors do affect your premium.
Also transmission can sometimes affect it too, auto = cheaper, manual = more expensive.
Oh yeah, and your gender do matter, female = cheaper, male = more expensive.
Wow?..... $5500 a year? That's kinda unbelieveable.
Even when I was 18 and drove a series 2 NA r33 coupe, they only want $3000 for full, $650 for 3rd party.