I've never had tanks cycle for weeks and weeks like most people do. Fish are pretty tough, a little bit of ammonia won't kill em. I just started that 13g tank for my gf, I used a few live rocks from my sump, dry sand, and some old dry rocks I had in a bucket. Threw a dottyback and a whole bunch of corals in there the next day. Fish is still alive and very active, and eating like a pig. Also all the corals are doing fine.
Personally I think people stress too much on the whole "cycle" thing. Throw a few pieces of live rock in the tank and some of that miracle crapp from Dr Tim's and boom ur done. I throw the fish in next day, or be safe and add em this weekend.
Good luck bro