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open the messaging app > open a message > at the bottom you should have an option to doodle
Indeed, you need a different keyboard app for that.
just browse the play store
https://play.google.com/store/search?q=handwritting&c=apps
https://play.google.com/store/apps/details?id=com.phatware.writepad&hl=en
https://play.google.com/store/apps/details?id=com.metamoji.mazecen&hl=en
http://blog.intuit.com/trends/5-handwriting-apps-for-taking-notes-on-your-tablet-or-smartphone/