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.

How does this work?

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.