This happens every now and then. Just this time rebooting my iPad doesn't solve it.
Any idea what caused this? Unfortunately I'm on the go and this makes safari practically unusable.
This is not a bug, it's a feature ;)
Just long click on the bottom right key of the keyboard, when the menu pops up, click Dock Keyboard.
You can enable that by dragging up the keyboard with this key (see the three little bars at the right?). Also, you can dock him back by dragging it to the bottom of the screen.
FYI, you can also split the keyboard, making it easier to type while holding the iPad.