"제 꿈은 소방관입니다."
Translation:My dream is to become a firefighter.
no this is right. you say it different in Korean than you do in English. For example "what is your dream?" would be something like "꿈은 뭐예요?" In korean you don't have to switch the whole sentence around you can literally just switch out "뭐" with what ever you want. In this case"소방관".
On TTMIK's recent live classes 현우 선생님 used "제 꿈은 ...-되는 거예요. " and he's a native speaker.