How do you do the symbol of the moon with the star next to it on Instagram?

[Paige]

Like all the cute little symbols people use for their bio's on Instagram?

[Cat]

Do you mean the star and cresent of Islam? I'm sure most of the users who use that symbol are muslim, and hopefully not ignorant of it's meaning.
http://en.wikipedia.org/wiki/Star_and_crescent

The unicode for typing that symbol is U+262A: ☪
Just type "& # x 2 6 2 A ; " without spaces for html (hex): ☪

If you are not muslim, you might be interested in more generic astrological symbols.
First quarter moon U+263d
"& # x 2 6 3 d ;" without spaces: ☽
Switch that last "d" to "e" to get the last quarter moon: ☾
http://en.wikipedia.org/wiki/Planet_symbols

Star outline U+2606
"& # 9 7 3 4 ;" without spaces: ☆
Black Star U+2605
"& # 9 7 3 3 ;" without spaces: ★
http://en.wikipedia.org/wiki/Miscellaneous_Symbols

Edit: if you have trouble, make sure you have the latest operating system upgrade installed and make your applications have been updated. You can also try to copy+paste these symbols directly without the Unicode.