I'm not a physician, but I think there are several reasons not to panic about your daughter's results. Since she had a cold, that can easily explain a neutrophil dip, typically for a few days to a week. Another reason is that a single lab test can sometimes be incorrect and her neutrophil count may come out higher on the next test. Finally, it's smart to follow the lead of her pediatrician, who thinks it's OK to wait for another test after her cold subsides. If he or she thought your daughter was in serious danger, more testing or a hospital stay might have been ordered.
However, I think it would still be wise to take precautions until you know her neutrophil level is safe. I know that vigilance for an active 3-year-old isn't the easiest thing, but if you have her wash her hands frequently, keep her away from obvious sources of infections like the cat litter box, and perhaps have fewer playdates, especially if other kid are sick in any way, then you'll be protecting her from further infection.
I hope that with rest and fluids, her cold clears up quickly, so you'll be able to check that her counts are normal.