Small Caps are capital letters in the height of small letters.
LinuxLibertine O provides those small caps, but they have to be inserted as special characters.
Illustrator supports a very convenient method to insert special characters: The Glyphs. You can find Glyphs at the "Top Navigation": "Type": "Glyphs.
These steps may help to get it:
- Make sure the cursor is within the textfield
- Open the glyphs
- Use the dropdown menu to chose "Small Capitals From Capitals"
- By double clicking on the letters of you choice they will get inserted
Use Linux Libertine O C.