Yes you should be able to email a PDF from iBooks. When you tap the arrow in the upper left the option should appear.
Maybe some basic troubleshooting steps will help.
Quit the iBooks app completely and restart the iPad. Go to the home screen first by tapping the home button. Double tap the home button and the task bar will appear with all of your recent/open apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus sign in the upper left corner of the app that you want to close. Tap the home button or anywhere above the task bar. Restart the iPad.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Or .... Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
You may want to consider deleting the app and reinstalling. Tap and hold down on the app icon until it jiggles, then tap the X on the icon. Tap the home button to stop the apps from jiggling. Download iBooks again.