Hedwig getting got just completed the raping of Harry's "protectors". Especially since she was never gonna kill off any of Harry's close friends Ron, Hermoine, Ginny, Neville, or Luna.
But honestly I think they dropped Hedwig because she was gonna weigh them down. It's bad enough she had to invent the Mary Poppins carpetbag so that they could carry all of that stuff with them as it is. And I think putting a live animal in the carpetbag would have been disaster.