Originally Posted by Nikineko
In broad terms you can practically do anything as a solo skit. The one thing you have to remember is to keep your audience engaged. Monologues can be great if you can perform something that isn't too inside the series.
This. You have to make it something non-fans will be able to understand. If they can't understand it, you've lost a chunk of the audience, even on something popular like Fairy Tail. (No matter how popular the series, there will always be people in the audience who don't know it...unless it's like a MLP skit at a Brony convention, of course.) Whatever you do, practice it in front of a relative or friend who knows nothing about Fairy Tail and see how well they understand your skit. If they understand nearly everything you're saying and doing, you should be good to go.
I did think of a few ideas:
~Erza has just had an argument with another character and is ranting about them.
~Erza feels sad for some reason and begins to sing a short song. (If you can sing)
~Erza has just won an important battle/got some high achievement and is excited about it.
~Erza is writing a letter to another character and reads it out loud as she "writes" it.
~Erza is reading a letter from another character and reacts to it.