"I don't like studying."
I'm not a Japanese native speaker, so I couldn't tell you with 100% certainty, but I don't think you are misunderstanding. It's objectively true that 嫌です is more formal than 嫌だ (or even やだ), but when it comes to comparing 嫌 with the negative of 好き, I think it's harder to draw the line and say "it's very casual".
The targeted answer for this question appears to be 勉強はいやです, so that's why の wasn't available. However, 勉強するのはいやです is an acceptable alternative, and closer to your incorrect answer; dropping the の is ungrammatical because は is used for connecting nouns and noun phrases, not verbs.