That's a great way to get cooked inside your rocket by blueshifted cosmic rays. You'll arrive at your destination ready to eat, a kind of cosmic jerky sent by the gods.
Space is filled with cosmic rays, mostly protons, going in all directions. Most of them have energies under 10 GeV (99.6% c). But if you start racing through that flux at a very high speed yourself, their velocity relative to you will be boosted in the direction you're traveling, and you'll briefly see a high-energy particle beam coming through the windshield before your eyes are cooked.
If you get going really, really, really fast, a similar thing happens with the blue-shifted cosmic microwave background.
