Is it normal that I am attracted to little girls?

That just shows your lack of knowledge in today's times. How old are you? I and others, 100% aware pedos don't need to look the 'part' to be one. You said people relate them to a mustache and greasy hair. Not true. With things like any recent news, the internet and lots of public outing of pedophiles (Enforcement officers, people who have 'nice' and 'helpful' seeming careers, working with children) it's actually a lot of suburban family types, who also think they did not fit a specific profile. In my experience with close friends AND studying, it's always the ones' you don't expect that were the predatory type/deemed unsafe. This doesn't place any pedophile in any superior box--far from 'typical' looking creeps taking children in the streets, committing an act of molestation, in a run down city. Same person internally. Just different ways they go about it and different risks in acting on their desire.
You seem to take pride in not acting on this or seeming harmful. As if fears of prison, being outed, life being ruined etc makes for great justification as to why you just haven't acted. Since it's evident it's not mental strength keeping you from doing it. You're complacent with the feelings of, you even ASK if it's normal, hoping to find someone just like you. Not a question of "IIN to fear help for this".. For most pedophiles, they just think they're not that dumb guy who is going to "go and get caught"..

Like I said, your mere presence IS enough, because mentally you are not a safe person to be around and you take no proactive measure to find the cause of a perversion. As said; you live with it.. you're totally complacent with it. No one demands get therapy from someone with a notebook, there ARE plenty of things you could do for yourself. For the lazy/weak minds.. "It's not that easy".. That's a lie and cover-up. Sexual release causes good feelings, so people with deviant thoughts will choose to indulge as opposed to stop or figure out the root. Which is an easier than people like to pretend. If someone has UNPLEASANT feelings; depression, stress etc. they'll go to worlds end/spend thousands of dollars, research until the sun comes up, just to make it stop/figure out what is WRONG with them.

Sexual release just feels too good and males are much more unpredictable/prone to senseless mistake with any sexual urge. We know this. Do you think every person sitting with their 25-life all thought they'd be there? Any rapist, person who violated a child/even killed them just to keep it a secret and impulsive mistake all thought that was the intended plan?
Just like any desire of that nature, it's only a matter of time before you make any mistake, big or small, that a lot do. Even downloading porn, there's a COP with his life in ruins right now because of just that, which he even claimed too, was a thought/spiraled into an immense desire that he acted on. Because it always does, for those who won't acknowledge it as any issue. Just something you justify as being born that way?
You won't live your entire life simply 'thinking' and just fantasizing. So you are always a threat, as long as you're living with it. You claim you don't indulge in kiddie porn, even though you name specific porn category the fantasy, you stated your attraction, so in any public situation, you are doing/thinking of something that caused the revelation you enjoy "little girls" (as you put it) So an undercover pedo, thinks just thoughts and feelings are ok, huh? No. It should be OK and parents shouldn't be worried, right? I can guarantee not one single parent would choose having you around their children, knowing your attraction, not one. It has nothing to do with apparent paranoia, it is common sense and taking every measure to keep their child safe and innocent. Knowing you'd potentially be getting a hard on and fantasizing about their child later at home, is just a disgusting act and feeling for any parent.
Pedophiles do not deserve the common decency/respect of, "But they should be helped and not chastised" -- No. They should act like the grown people they ARE and take control of their own sexual fantasy and control it/diminish the problem, because there is absolutely one and it's all choice. If you ever have children/a daughter, I assume she's 100% safe and it is somehow different.
I've myself, since the age of 8, had my own sexual demons--internally--that bleed into my adulthood, but I took control of even the mere thought, every single time it would become a thought. EVERYTIME. I absolutely had no control of what it specifically was/why it popped in my head; because that can be nature vs nurture, but I never made the choice to indulge in any fantasy regarding it, never kept the desire alive, and would never choose to keep it a desire. To diminish a sexual urge, that is unnatural in every single way (and not something you're just "stuck" or born with) is all choice. There's a multitude of reasons people can have unnatural "attractions to" (that aren't 'normal'; ie, pedophilia, violence, necrophilia, incest, bestiality ect) but there IS innate traits within people that separate a deviant person from a sensible person. Innate keyword, if you're not one who can find the knowledge about themselves and have the strong will to conquer things that are wrong, cause grief, a large amount of guilt and or shame (or don't feel any of that at all, even while fantasizing the acts against an adolescent) psychologically, you are also not someone who will live so sensibly/by any standard of completely civil /right actions your ENTIRE life.