Every wood will leech a little. If you go outside and grab a stick and put it in water, the water will turn a little brown after some time. Some trees will turn it very brown.
Dowels are made from trees with lower tannic acid, and so they don't leech as much and it's lighter colored.
Obviously do what you are comfortable with; I just want you to understand what you're seeing so you can make an informed decision. Dowels aren't great for their feet if given as the only option. That's more of a health risk than the tannins.