"My hobby is photography."
Grammatically, it is correct. However, Duolingo likes maintaining the word order if possible. Maybe these examples might help demonstrate a different choice of word order:
What is your hobby? "My hobby is photography. (我的爱好是拍照)"
Why do you take so many pictures? "It's (taking pictures is) my hobby. (拍照是我的爱好)"
Native speaker here. 摄影 is actually the proper term for photography (like it would be the main translation in a dictionary). 拍照 is a more casual way of saying it, literally meaning "to take photos". So really, the sentence says "My hobby is taking pictures."
影 doesn't have to mean movie. Strictly, it just means "shadow". Also 拍 and 摄 are used to describe both taking pictures and shooting movies/videos (e.g. 拍视频 to take a video).