Special Character Auto Numbering

You can use the Autonumber feature to insert a glyph instead of a number (that's how bullets work, after all); however, you cannot use the number building block to "increment" glyphs. They're two very different things and FM will not recognize what you have as a number.

There are, I think, typefaces that provide numbers with backgrounds (either full or half circle). If you had one of those you might be able to do this as long as you have a character style applied to the autonumber that specifies use of that typeface. 

Edited to add: This article discusses number typefaces, and one or more of these may be able to do what you want.

As a side note, the glyph you provided as an example is part of the dingbats character range and you would only have the "numbers" 1 through 10 available. This may or may not be an issue for you.