"These files need to be organized.I'll get on it right away."
Would it be correct to use it with a gerund?
"There is a lot of work that needs to be done. I'll get on writing a report first."
Merriam-Webster's Learner's Dictionary
get down to (something)
to start to do (something) : to begin to give your attention or effort to (something)
▪ It's time to stop delaying and get down to work. ▪ Let's get down to business.
Getting Started on Writing a Resume!
The first question that occurs to each one of us when we get down to writing a resume – “Where should I start?”.
Writing business letter
Alright, let's get down to writing a proper business letter.
If you would scroll down Merriam-Webster's Learner's Dictionary, there will be the definition
" get on (something) US : to start to do or deal with (something)
▪ “These files need to be organized.” “I'll get on it right away.”
I put a straight forward qustion about it. Why would you be coming up with answers to another phrasial verb?
You wrote: I actually meant started doing something.
So I just told you a phrasal verb which means "to start to do (something)."
"get down to writing a proper business letter"
This is an example which might help you understand how to use "get down to."
Does "get on with something" mean "to start to do (something)"?