Whiplash is quite capable of causing problems even in low-speed shunts - especially if the 'bump' is unexpected (i.e. the driver is completely unaware of an impending collision).
Osteopathy may be able to identify where things have gone wrong, and may be able to fix them so that your body goes back to what it was before the accident. However, there is less robust evidence that osteopathy can make a definite contribution to trauma induced neck pain.
However, don't listen to people who tell you that you will always have a problem, or that you need to wait for 6-12 months to get any improvement!
Checkout this video for a simple demonstration of what happens to the neck in a rear-end-shunt.