The thing is, I was being facetious.
But, when this question showed up in my stats, I started thinking a little more seriously about what "normal" meant in this context. If we apply the technical definition of "normal" and look to see whether it's "the norm," or typical, the answer would appear to be yes.
Initially, she tried to discourage me from mentioning her cartoon character crush, but then she turned to a different approach: diverting me with tales of her friend's crush on this guy, who is apparently sort of a claymation character or something.
|Whatever that guy's name is from|
How to Train Your Dragon 2
Does this mean it's normal? Not necessarily. But it surely means that if you're asking this question, you're not alone.
And, if you're thinking about your crush in terms of a fictional character, then I'd guess that you're a good bit closer to the normal end of the spectrum than those (seemingly many) folks who mix the character with the actor, attribute characteristics from the role to the actual person and then deem themselves "in love" with celebrities. I mean, you know the character, right? You may not have met him (because...well...he may not exist), but you know who he is.
So, you know...enjoy. Just don't lose sight of the lines.