It's untouched ground, there's a minimum threshold for being a self replicator, but no minimum threshold for getting called 'operating system' (I myself can probably write an 'operating system' in a week or two, or even in a weekend, depending to how little we consider to be an operating system), and such replicator - I am speaking of supervised self replicator, i.e. largely under remote control - is economically ineffective compared to regular, staffed factory. A replicator is no magic - it is a moderately big complex of factories, with automatization of even the rare tasks that would normally be much much cheaper to perform with humans - there is literally no commercial incentive to design something like that, considering that it would cost billions to design. More, actually, because the hardware of the first original is going to be awfully expensive.

I must make clear what replicator I am speaking of. A practical one, which is to significant extent remotely controlled, and for which much of the difficult to manufacture electronic components (CPUs, memory chips) are shipped from Earth (they are lightweight). Such replicator would require multiple extremely heavy launches to get there, it would be very fragile, and it would grow considerably slower than even remotely wise investments. So you'll probably be better off simply doing something else and going to moon later.

It is not really glamorous awesomeness by any means. It would largely rely on existing CNC machines and existing robotics, it would be huge, it would be messy, and it is going to break down once in a while at first (with a bit of luck that may be resolvable with remotely controlled robot, in a manner similar to trying to solder chips onto a board by holding them with chopsticks).

edit: tl;dr; it can be done, it wouldn't be the most complex task mankind ever done, and it is going to suck.