http://www.qib.com.qa/en/media-centre/news-updates/QIB-Enabled-Online-Pu...

I suppose QIB debit card can be used for online purchase. Please refer the above link.

Sorry, I do not have much idea about credit card at this moment.
I cancelled credit card from three banks in 2008. I though I should be out of credit card at least from the date my first child's birth.

How ever it's your choice. We are only suggesting.