I know this is kind of an old post, but I just came across it.
That is a Q400. The Q300 has 2 pick ups. There are also a Q3000 & Q4000 that have bolt on necks, cheaper electronics and I believe each pick up is not independently switchable... Cheaper version.
I have a Q400 prototype which, like most prototypes, has a little better materials than the production models. Mine has PJ Marx pickups for example & I believe a different Kahler. I did a lot of research but it is hard to find too much information on these. I came across someone who was supposedly a retired engineer from Gibson who said these were made as an answer to the "super strat" guitars in the '80, (such as your Jacksons, Kramers, etc) but didn't sell real well because they have that Gibson sound & everyone wanted that thinner "super strat" sound. Then when bands like Guns & Roses came along & everyone saw them playing Les Pauls people started wanting those. But most people didn't want a strat like body that sounded like a Paul, they wanted the real deal & that look.
I haven't been able to find out how many of these guitars were made in production, but my prototype is apparently one of four. (two red & two black were made) It's not like I'm sitting on a gold mine or anything because they aren't really "saute after" or anything, but it is rare & unique and it sounds & plays good. I mean it's a Gibson Custom shop guitar, right?
Hope that was some help, & I hope you're enjoying that Q400. I personally think it's a pretty cool guitar.