I would say no. 2ft x 2ft really is pretty tiny, and although this wouldn't be a problem in the day when the bun is out of the hutch, spending the night (12+hours) in a tiny space where it can barely hop around would not be very nice
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Minimum guidelines from the RSPCA say absolute minimum should be 5ft x 3ft, and should be tall enough for the bun to stand without it's ears touching the top. The cage should be at least big enough for at least 3 consecutive hops in any direction.
I would also recommend getting a double storey one, but thats just preference
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Have you got a run? If you'd prefer, you can give your rabbit exercise time in a 'safe' room in the house, if you want to save money on buying something extra which can be quite costly. I love putting mine in the run, though, because they just adore the grass and do not stop binkying for the first 20 minutes or so lol. Or will your bun have the run of the garage too?
They'll need a good 3 or 4 hours minimum exercise time outside the hutch each day.
Building your own hutch might be a good way to go! Or converting a shed. My Dad started by building hutches for my two buns, and now has moved them into a converted shed with different levels and boxes etc., and he built them a run. It shouldn't cost any more than a decent hutch would cost to buy, and you can make the good dimensions, which a lot of bought hutches just don't have!
Your bun looks soooo cute btw!
Jen