An online study, the participants had the full choice to fill the questionnaire and they signed (a check box) that they agree for sharing their data in the study. In this case, Do we need an ethical approval ?
The answer to the question "do we need ethical approval for X study" is ALWAYS yes. The format is irrelevant. Your institution's ethics review committee will have a category for "minimal or no participant risk" which will often have fewer detailed requirements for submission in instances such as the one you describe.
Nevertheless, the issue is about /independent/ assessment of ethical research. Even when you believe your study guarantees /zero/ risks, you must have an independent panel validate your method.