There are a couple small problems with this. First, this trick is already mentioned well above, called the "Time Travel" trick. The next problem is when you move your clock back, nothing new happens to your fish. You can get them pregnant, but they will not age, nor have babies until after the clock on your computer pes the time that you fast forwarded it to.
This is how I kept my fishies alive for the first week or so playing the Web version. As long as I bred the fish and fed them up until the next time I would be on, time traveling forward then resetting the clock back to correct time before leaving it, the fish would never die of starvation, even if I was away for 12 hours, because according to the game clock, they had been fed routinely over the previous 12 hours (while in time travel mode).
Oh, and if you were wondering, the time involved for fishies to be born is 1 hour 40 minutes, or 100 minutes. This is 5 minutes per unit of age (only in fast mode, and the online version).