"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".
I think it's because -입니다 can also mean 'to be'. So 소방관 (firefighter) + 입니다 (to be) = 소방관입니다 (to be a firefighter)
입니다 doesn't mean "to be". If I translate "My dream is to become a firefighter." into Korean directly, it may be "제 꿈은 소방관이 되는 것입니다"
~이 되다 = to be