It’s normal for the mother doe to hop into her nest when someone approaches. This is because in the wild, rabbits are prey animals. Their natural instinct is to run away. The mother is probably very sensitive about her baby. She doesn’t want anyone to mess with her baby – much like human mothers are protective and sensitive towards their young. The mother knows where the baby is, unless she lost her scent, which is unlikely, unless you mess with the baby too much – which I recommend that you not do. But, since the doe is a very young mother (6 months of age is typically not recommended for rabbits to breed. I usually advise waiting for breeding until at least 9 months of age, if not a year, depending on the breed of rabbit.), there is a chance that an accident could happen. New rabbit mothers, just like many human mothers, are somewhat inexperienced at being a mother the first time around.

But, instead of worrying whether it is a problem if the mother steps on her baby, it is better to take precautions not to startle the mother in the first place. When you approach her cage/house, walk quietly and slowly, taking great care not to make sudden, loud sounds or movements. Talking to the doe softly and soothingly often helps. Do not try to mess with the baby unless you absolutely have to. Like I said, the mother is very protective and sensitive towards her baby, and she doesn’t want you to mess with the baby! Don’t mess with the doe more than needed, either. She just gave birth, for crying out loud. Would YOU want to be messed with?

Does feed their young during the night, for only a few minutes at a time. It’s very likely that you won’t even witness the doe feeding her baby at all. Does also need more feed during this time, because she is making milk to feed the baby. I typically advise people to install a J hopper feeder in the cage, and provide unlimited free-fed rabbit pellets at all times. The mother will eat what she needs to in order to nourish herself and the baby. These feeders only cost a few dollars at a farm supply store, or the pet store. (Actually, I use them full-time for three of my rabbits, and they work great.) Make sure the doe has plenty of water, too. And, as I said before, monitor the baby and its development, and watch the doe, too.

I hope this helps!
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I’m a 4-H member, and a rabbit leader in my club. And I am mommy to five happy and healthy bunnies!

It’s also not uncommon for mother rabbits to jump into their nest when they see someone coming. They’re just nervous but yes, they could accidentally injure their kits. Approach the cage quietly and distract the mother with a treat (carrot, apple slice, lettuce, etc.) if you need to do something with the nest.

Regarding survival…as long as the baby is quiet, Mom is doing her job and there is no reason to worry. Mother rabbits nurse their babies only at night, so don’t be concerned either if you don’t see this happening.
References :
"Barnyard in Your Backyard" by Gail Damerow

get your rabbits fixed and you wont have this problem anymore, now will you?
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