1) I'll take note on that is not correct. We don't 'take note on something'. It sounds like the article 'a' should come before 'note'. There is no clear meaning.
2) I'll take note of that is a correct and idiomatic sentence. It means 'I'll pay attention to and remember that'.
I'm afraid you might be confused with 'take a note of', 'take notes on' and 'take note of'.
(BrE) take a note/notes of X = record X for the later use (AmE) take notes on X = record X for the later use I took a note of everything Mr Blair said. I took notes on everything Mr Bush said.