'feel it doing' is correct and can be used in written English.
It is typically used as an idiom to mean 'experiencing the effects of something', often in a positive manner. For example: "I'm already starting to feel it doing — the new exercise regime is really helping me tone up."
Exact(1)
So as I'm kneeling on the belt, I can feel it doing a lot of damage to my pants.
Similar(59)
"You know, I feel it does," Chandler said.
It didn't make me feel — it didn't make me feel wonderful about my relationships.
They feel it does not listen to their ideas.
If you cannot feel it, don't stick it!
If you feel it doesn't apply to you or your situation, skip it.
After that, he felt it did not.
Billy felt it didn't make "good copy".
I felt it didn't give me a way in.
Try to feel it while doing so.
I did feel it but I didn't show it.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com