Translation:My little sister wants a big room.
No, бо́льшее is used for neuter nouns. Ко́мната is feminine, so ‘larger’ is бо́льшая.
You can only distinguish «больша́я» ‘large’ and «бо́льшая» ‘larger’ by stress, which is not written here. However, Duolingo has audio which probably says «большу́ю» and not «бо́льшую».
Also, бо́льшую комнату́ sounds somewhat bookish in this context. I think «ко́мнату побо́льше» would sound a more natural translation for ‘a larger room’ in most cases.
(BTW, больша́я/бо́льшая is one of the cases when Russian speakers would actually mark stress — although often by using a boldface or capital letter, since it’s hard to type the áćúté accent on most Russian keyboard layouts.)