No, these camels were very much older, or rather, not nearly as old as they should have been. The problem camels are those mentioned many times in the Old Testament as possessions of Abraham, Jacob, Joseph and others.
Two archaeologists from Tel Aviv university have performed radiocarbon dating of old camel bones in Israel and Jordan. Being able to identify domesticated animals from signs in their leg-bones that they were beasts of burden, they have concluded that camels were not tamed to use for carrying men and goods before around 1,000 BC. Since this was approximately 300 years after the Exodus from Egypt, itself 400 years before the Israelites came to Egypt, it means that the patriarchs of the Old Testament could not have used them.
It seems ironic then, that the humble camel should bear evidence to the questionable veracity of the bedrock of the Bible which is the Book of Genesis.