'do doing' doesn't exist as a pair of words together.
Did you mean something like, "It's going to take some doing", which means 'It's going to take some effort, or a lot of effort".
Example: "We have a lot of work to complete before the day is over. It's going to take some doing". ie We need to do a lot of effort.
'do thinking' only exists very informally, if at all - "I'm going to do thinking about that" ie I am going to think about it/I'm going to give it some thought. Only very rarely do I hear it. It sounds not that good and awkward (to me). You would qualify the word 'thinking' with something like 'a little', 'some' etc. , "I'm doing SOME thinking about that". "I'm doing a little thinking about it".
Example: (A) "Are you going on holidays later this year ? (B) I'm going to do some thinking about it. (I'm going to give it some thought before deciding)