The first sentence (antes de levantarme) is correct, the other sentence is not correct. Notice that both verbs are in infinitive form.
The second sentence should a "que", "antes de que me levanto"... though it does not sound completely natural to me. At least not in this context. I would not use it to express "likes". I could use it to express habits, though. "Leo un capítulo antes de que me levanto todas las mañanas" (I read a chapter every morning before I get up".
Надеюсь это Вам помогает.