是不是没有learn doing，只有learn to do?

错，learn既可带动名词也可带动词不定式作宾语。不过就我所知，learn to do用得更多一些。
如：
We learn to crawl before we learn to walk.
我们学会走路之前先要学会爬。
Do you learn swimming?
你学会游泳了吗？
另外接动词不定式时，常会加一个how,即：learn how to do sth 学习如何做某事。
Many young people are learning how to drive a car.
许多年青人都在学习如何开车。
I’m going to learn how to repair machines next year.
明年我将学习如何修理机器。