I've been wondering about red eyed bunnies lately as my Millie has red eyes and noticably scans.
She's not at all dippy though
but does get freaked if you sudden come into her line of vision or if your shape changes ie your carrying something.
From my siggy you can see she's not white does it mean she may have been crossed with a REW and will her eye sight go worse with age then?
Lucyhp - Hope your bunny is ok and it's just the red eye's making him sway, Millie sways, her head goes slightly up and down and she kind of leans to one side when she scans.