It is probably really easy to scoff at the notion of depression in pre-schoolers and write off irritability (which can be a manifestation of sadness) as kids being difficult, but there is a qualitative difference between being crabby or sad and clinically depressed. The NY Times writes:
parents tend to feel responsible. Children of depressed parents are two to three times as likely to have major depression. Maternal depression in particular has been shown to have serious effects on development.
Keep in mind that these are just probabilities and stats and don't mean that every child of a depressed parent will be depressed. The Times continues:
But it’s easy to overstate the role of maternal depression. “Most kids of depressed parents don’t get depressed,” says Arnold Sameroff, a developmental psychologist at University of Michigan’s Center for Human Growth and Development, who has studied children of parents with mental problems.
The bottom line with this issue is that you need to trust your parental intuition. If you suspect your child isn't just being a 3 year-old, ask a professional.