How do you type a hedera/fleuron symbol in InDesign using less effort?
You are right that there are some Unicode characters that will work on Windows with Microsoft programs but not in InDesign. I worked for a company for a while that had a glyph as part of their name, and I used a couple of tricks. Make sure you always use a font that contains that glyph, then assign a keyboard shortcut to insert the glyph. I also set up a custom search and replace to allow me to type the name without the glyph and then run a search/replace that added the glyph in.
In your case, assuming you are using this character to designate the end of a paragraph, or sentence, etc., I would create a paragraph style using GREP styles, that will automatically insert the symbol before a paragraph return (for example) in paragraphs using that style.