Should I take time out to deal with my depression? Can I take disability?

Depends. If the depressive episode is severe and compromises your function at home and work, then addressing the depression becomes a high priority. As far as taking leave or disability, that should be a discussion between you, your physician, and your employer.
Yes, it depends. If your depression is impairing your functiopn it might be better to take time off than develop a bad reputation. If you have a disability policy sometimes there is a time period that you need to be out /ill before coverage kicks in.