As missyscove mentioned, not all animals at a shelter are necessarily listed online (especially if they have a lot of that type of animal), so it's definitely worth looking into more.
I got a Holland lop and a Lionhead when they were 8 and 7 weeks old, respectively. I love them to pieces and it was a nice experience, but I found there's definitely something to be said for adopting adult (or young adult) rabbits!
~ Babies can be difficult or impossible to fully litter box train (as in getting them to do all their peeing in the box) until they're older; many adults come already trained. I adopted a rabbit a couple weeks ago who's a little over a year old, I think. He had shredded paper (ugh!) in his litter tray at the shelter... I brought him home and put a dishpan with pine pellets (kiln-dried) in it in his temporary x-pen set-up and despite the change in substrate, he knew right away that that's where he's supposed to potty. He did leave a lot of stray poops briefly after coercing me to expand his territory faster than I should've, but that died down after a couple days and now he gets 95% of his poops and all of his pee in the box... better than my girls have ever done!
~ It's common for babies to leave cecals around instead of eating them all (a combination of producing extra because they get fed extra pellets and being forgetful because they're so young) - Gaz, my Holland, left at least a few a day at first... though by 4 mos or so, it had pretty much stopped and by the time she was spayed at 5 mos, she never left them any more. Cecals are stinky, smooshy and gross, plus they can get stuck in fur if a bunny sits on them. Eww!
~ Spaying/neutering is nerve-wracking. Even knowing that with a qualified vet, there's a 99% chance of things going smoothly, how can you not be worried by that 1% chance that you might lose the bunny you've spent 2-4 months getting attached to? I was so nervous! Everything went perfectly with my girls spays, thankfully, but it was still a very worrisome experience. The next couple days were bad, too, as Nala kept licking her incision and I had to put a gauze pad over it and then wrap vetwrap around her tummy and the girls didn't want to eat because of the lingering nausea from the anesthesia so I had to force-feed them Critical Care - not fun!
~ Spaying/neutering can be expensive if you can't find a low-cost clinic that does bunnies (most don't). I payed around $465 for two spays (including incidentals and metacam to take home).
~ Bunnies tend to need to grow into their personalities - with an adult, you can see their true personality to begin with. Nala and Gaz didn't really display much personality at all when I picked them out at the breeder's place, though I somehow intuitively knew to some degree for reasons I can't explain... their auras, I guess
. Their personalities did develop and evolve more as they grew up, though.
By contrast, Norm was full of personality when I met him at the shelter. When I brought him home and he'd had all of a few hours to settle in, he was already acting like "why wasn't I here all along??"! Within a day, he'd convinced me to let him out of his x-pen early (he was crashing into the sides trying to do binkies in there - broke my heart and I had to drop what I was doing to bunny proof a larger area for him) and would follow me around the bedroom/hallway area where he's allowed, licking my ankles at every opportunity, and then wait at the gate when I went to the rest of the apartment. He's actually more outwardly affectionate than the girls I raised from weaning age - a total cuddler! The girls really don't act happy to see me unless I have food for them, lol.
While I could never regret anything about Nala and Gaz, I definitely wouldn't want to go through the "baby" experience again! Getting a full-grown cuddle bunny who came home with impeccable litter box habits is a wonderful thing.
As a note, shelters/rescues DO sometimes get very young rabbits, pregnant does or does with a litter. They don't adopt out the babies until after they've reached spay/neuter age and been fixed... however, they very frequently place "immature" animals (as in too young for getting fixed and, if applicable, vaccinated) in foster homes.
If your wife would be interested in fostering, it would be a great way to get a feel for what juvenile rabbits are like... plus, if she fell in love with one of the foster bunnies, she could adopt them when they were old enough. With that route, you'd get to give a rescue bunny a home, get them a dirt cheap spay/neuter surgery for the low cost of the adoption fee AND she might get to raise the rabbit from a baby... and shelters are always looking for volunteers/fosters. (Volunteering at the shelter would also be a way to be around the little ones a lot, though that's a big time commitment.)
While some animals are placed in foster homes to recover from illness or injury, I learned in the foster orientation class for the HSPCA that the vast majority of animals they send to foster homes fall into the "immature" category. It may vary from shelter to shelter, but the Houston SPCA's foster coordinator does NOT assign animals to people who have volunteered to foster - you pick whichever animal(s) you want out of the ones they're seeking foster homes for.