。
We went to bed early in order to get up at dawn.
Literal
We [topic-は] dawn [at-に] get-up [for-the-purpose-ために] early slept.
~ために ('in order to, for the purpose of,' with a verb) is the standard purpose construction. 明け方 ('dawn, daybreak') is a native-word compound. に marks the time of waking. 早く is the adverbial form of 早い ('early'). A simple sleep-schedule purpose statement.