Considering the party is going to be at a public place and at least chaperoned by you, why not? I think the venue is neutral enough. Invite the parents of the girls to help out if you think that will keep things on the up and up.
Now, if this were a house party in the basement, I'd probably nix the idea for fear of hanky panky like spin the bottle (showing my age, I know) or other teen hormone maddness. I have no desire to have parents getting out of joint if they should find out something happend at the house under my watch.
However, the fact that it is a planned event at a particular public venue, to me, makes this an okay deal to invite both boys and girls. If you think keeping tabs on everyone will be a challenge, enlisting other chaperones is A-Okay in my book.
I have pretty conservative parents, especially where dating was concerned, but even I had co-ed parties. Now to think about it, all of my parties but one (my 13th was a girl sleep-over) party were co-ed parties. I think the key to success and clean fun is venue and chaperones.
And last but not least...no you are not over-reacting as others have said. Your concerns are valid ones. Kids are doing so much more "dating" and socializing earlier and earlier. So it's never too early to have a game plan in place for questions like this. Things do and can happen...but probably not at a Lazer Tag party away from home.