First, I don't know the expression but I can feel what that means like kinda :)
Korean ppl are good at making new onomatopoeias and mimetic words. In other words, they often express their feelings and how it looks like in their own ways without using expressions from dictionary
Speaking of common expressions on dictionary
모락모락 김이 나다 it's steaming
모락모락 expresses how the steam comes up
새록새록 기억이 떠오르다 I can recall the memories
새록새록 expresses how the memories are coming up in your mind
Like this, it's a bit difficult to explain this kind of expression as only korean uses in this way :)
Back to the main question, 도록도록 sounds like poping sounds for me. I don't mean I'm correct. I'm just guessing.
When air is stucked in your eyes it makes poping sounds when it comes out of the eyes.
I hope it is helpful for you :)
TMI, Languages are changing so I hope you spend time to explore new words like slangs from time to time. If there is a language that makes new words at the fastest pace around the world could be Korean language of others. This is just my opinion haha :) bye