Hi there Dots,
Yes, that can happen with Prozac. Quite often there can be a dip in the mood during the initiation of treatment. Usually this lasts for around 2 weeks before the drug "beds in". After which, beneficial effects start to kick in, although it can take around 4 weeks for it to become fully apparent.
These type of effects tends to occur with most antidepressants irrespective of drug category although with varying intensities which of course would be specific to the patient. General consensus would be to try to ride it through if you can, but of course let your medical team know of any untoward effects you may be experiencing no matter how small so that they can stop treatment with Prozac if need be.