Young rabbits that are just weaned are at much higher risk of illness because their gut flora is not fully established and any stressful changes (e.g. being removed from mum, siblings, changing house, temperature, sounds, smells etc) are all very stressful events for a prey animal. It's not simply a case that as soon as they are not drinking milk from mum, they can be removed - they need to be left longer to allow their bodies to mature in a stable, change-free (and hence stress-free) environment.
Because they are so immature, at 6 weeks old it is possible, but harder for them to cope with this and the risk of them getting ill through stress is much higher. There is a very high incidence of coccidiosis in baby bunnies of this age as well, because their guts are not mature and unable to cope with the sudden changes. It's not uncommon for babies to die in the 6-10 week bracket because they don't cope so well with all the changes. Of course this isn't the case with yours, which is brilliant, but it's a much higher risk.
The longer they can be kept with mum (without becoming sexually mature and making her or their siblings pregnant), the more opportunity their little bodies have to get stronger and the lower the risk of them becoming poorly and stressed out.
So yes, they may be 'ok' but there's a higher risk that they won't be...and it's unkind to separate such young babies from their mum - just like it would be unkind for me to shut you outdoors in shorts and t-shirt at this time of year. It might not kill you but it certainly isn't very kind so shouldn't be encouraged.
Hope that helps