Is there a way to outline Japanese dots in a border.
What do you mean by "outline?" Do you want to put a stroke around each dot, or change the dots into individual vector circles the way outlining type makes vector shapes from letters?
Copy paste your object in Illustrator.
Outline it (flatten transparency with outline stroke option ON + get rid of the transparent path in isolation mode or using direct selection tool)
Copy and paste it back in Indesign.
Here you go...
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