Method 1: You need to create indesign template (".indt") first which needs to cover all the paragraph, character, object, cell styles, swatches, etc. then save and use it.
Method 2: Create character style in one document and the load the styles from the corresponding document whenever u needed
What you can do too, is the create all the char styles in a document. Close all documents and load the char styles form the doc containing all the styles you need (para styles and char styles).
That way, all newly created docs will have all styles incorporated.