I always prefer getting up early ,rather than going to school without breakfast .

我总是喜欢早起，而不是不吃早餐就上学。

rather than 介词短语，意思是"与其"、"不是"。
rather than 与prefer连用时，rather than前后结构要一致。
如：
I'd prefer to go in August rather than in July. 我愿八月去，不愿七月去。

或者本句：

I always prefer getting up early ,rather than going to school without breakfast .

前面是prefer doing ...（表示更喜欢、宁愿）
所以rather than后面也要用doing sth.的结构

但是，需要注意：
当prefer后跟不定式时，就必须用：
prefer to do sth. rather than do sth.“宁愿做...而不做...”

prefer后面得接ing啊.....

比起不吃早饭去上学，我喜欢早起。
would rather+动词原形
rather than+现在分词，因为than是介词，所以其后的动词要用宾语形式

prefer doing sth
rather than的前后动词形式需一致 所以也用ING