The quad rail should fit well as has been said but unless you are dead set on it asap it is probably not the best option. Main reason being, well handguards, rails, etc.. are probably the faddest of all fads that infiltrate the AR industry and sickness. Currently quad rails seem to be on the outs and the newest craze seems to be with the Kemod or M-Lok type handguards. Most of these I have seen are equipped with a top Picatinny Rail, which of course you have on the quad rails. Point being, why not have the best of all possibilities by looking at some of the newer options as these can be adaptable to whatever attachments you prefer. At the very least next time you are at your LGS or the next gun show pickup a few quadrails and let the feel have a say in this, if you haven't already.
Here is an opinion piece that is dated but I think gives you some perspective about all of this craziness. BTW Midway is a great place to start your research and for the price of this quadrail, newer options are pretty much the same in price.
Keymod vs M-Lok: Which Will Set the Standard?