Where is the Apple logo?
The Apple logo is, obviously, trademarked by Apple — so they would never have accepted on the App Store an application that used it. Besides, it is not technically a valid unicode character, so it won't be compatible with every computer (particularly PCs).
If you want to add it to Uniconsole anyway, you can do so manually: just tap-and-hold the apple below in Safari until a menu offers you to copy it:
Now launch Uniconsole and tap-and-hold an empty button on the home page; a dialog box will offer you to memorize your favorite. (Make sure to tap an empty button, or the contents of your pasteboard will be overwritten.)
How can I get more symbols?
Version 1.2 and up of Uniconsole includes pretty much every single unicode symbol that can be displayed on an iPhone. But, if you find something missing, you can add your own favorites to the application's home page: just copy a special character from another application (e.g., by tapping-and-holding a symbol displayed in Safari), then launch Uniconsole and tap-and-hold an empty button on the home page (make sure it's an empty button, or your pasteboard's contents will be overwritten).
Make sure you copy a single character in Safari before launching Uniconsole: if there are several characters in your pasteboard, Uniconsole (as of version 1.2) will only copy the first one — that includes any spaces that may have been copied alongside the special character you wanted.
For instance, if you're looking for an unbreakable space ( ) for your blog posts, you can select and copy this character: “ ” and add it to your favorites, but you have to make sure that you don't select the quote marks along with the space.