You MUST carry the valid passport or the valid national identity card that you mentioned on the IELTS application form.
If you are taking the test outside your own country you MUST mention your current passport number on the application form and take the SAME document to the test center on test day.
To find out the exact requirements for the day of the test, visit the official page at:
You can only take pens, pencils, and erasers into the examination room. Anything else that you need for the exam will be provided to you by the staff at the test center.
For more information, visit this official FAQ web page: