Don't listen to anybody being an idiot. A 13 year old is already pretty healthily sexual, especially if they're girls. It's not like you're robbing the cradle because they're 3 years younger. You've had 3 years more life experience than her, but if you talked to her you'll see it's not a hugely dividing difference.
Just treat her like you would any other girl. Just be your nerdly self (based on that Mikuru inference you're definitely a nerd). If she doesn't like it, that's her problem. Don't go ranting in her ear about how Lucky Star is a funny anime and how most people don't get it or anything, but don't advertise yourself as something you're not.