What a surprise! I'm glad she had everything all ready for them and made them a nice nest. It's likely this isn't a first litter. Not always, but usually first time mom's don't care for the babies very well.
It can be hard to determine a peanut from a runt sometimes, even for experienced breeders. To me it looks like it could
possibly be a peanut, but it also looks like it may just be a runt. I think if there is any doubt, that it is best to give it a chance and keep a close eye on it. If it appears to be doing alright and is feeding well, then it's a runt. If it's skinny, lethargic, and not thriving, even if you are assisting it's feedings with mom(if needed), then it's probably a peanut.
That's quite a bit of fur on those babies. Looks like mom must have gone a couple days overdue. Usually they are born without fur. I agree that you are going to need a different nesting box, or you risk them crawling out, getting separated, and cold(not a good thing). I would suggest using a box with sides high enough to keep the babies from crawling out, but low enough that mom can still hop in. A shoe box or other cardboard box will work. For my 2 lb dwarf doe, the nest box was about 9x12x4(front) and 8(back). This gives mom enough room to move around in but small enough to keep the babies from being able to wander off too far from the center of the nest. Next put some carefresh bedding in the bottom if you have it, or you could even do layers of newspaper. This is to absorb any urine. Add any extra hay that might be needed if there isn't much hay in the nest that your doe already made. Next scoop the top layer of the nest that the momma bun made, with the hay, fur, and babies if they are secure in there(or set them aside somewhere safe until done), and set on top in the new nest box. You want there to be a bit of a hollow towards the back of the nest box where the babies can nestle down into the fur to keep warm. Next, place her litter box where you think she is most likely to want to go, and the nest box in the opposite corner, though you may need to switch if she seems to be using the nest box to pee and not the litter box. Hopefully she doesn't do it in both. You want to keep the nest box clean. If the hay is getting soiled then you will want to clean out the soiled parts as needed.
Mom will usually only feed once or twice a day(morning and/or evening), and usually 'ignore' them the rest of the time. You want to check the babies at least morning and evening for full bellies to make sure she is feeding at least once a day, and to make sure mom is cleaning them and stimulating them to pee. If the bellies look full before they have been fed, she may not be stimulating them and you may need to take over using a warm q tip and gently stimulating near the genitals. You may just want to go ahead and do it anyways. I did with my litter just so I knew it was being done and to avoid any problems from occurring if mom wasn't doing it. Also good to check their noses to make sure they aren't crusting over. Be careful when handling the babies. They are quite squirmy and can literally pop right out of your hand. Best to do any handling close to a soft floor.
Full milk belly
You also need to start gradually increasing mom's food over the next week. She will need more pellets while nursing the babies. You are basically working up to unlimited pellets, but also make sure she is eating hay as well and always has it available. The type of pellets you are feeding is going to matter as well as she will need more protein and calcium for nursing. What type is she getting now?
At about 11 days their eyes open. If they aren't open by 14 days, you may need to very gently use a warm cloth to help them open(never force). Check the eyes to make sure they aren't goopy or cloudy. The bunnies also start exploring around this time, and once you can't keep them in the nest, you then remove the nest box. With a smooth plastic cage bottom, you are going to need to keep hay or something on the floor to give the babies traction so they don't develop problems with their legs. They also won't be using a litter box yet, so need something on the floor that will absorb the urine when they pee all over. I used towels(with no holes or loose strings or frayed edges) and just changed them out regularly.
You want to make sure there is soft leafy hay(thick stems are too hard for the babies to eat) for the babies to start munching on. I was worried about digestive issues occurring from pellets too soon, so I was more careful about when I let my babies get to them. I placed mom's dish higher up so the babies couldn't get to them easily, but mom could. They would get the odd one that mom dropped and I would give them a few more each day, but it wasn't until about 4 weeks that they could reach the pellets and were gradually eating more of them, and were eating mostly hay to begin with. I felt this worked best to help their digestive systems adapt to solid food. It's also good to keep checking their bums every day in case they develop mushy poop from the pellets, as the poop can dry on the opening and plug them up.
You may be able to *** them now or in a couple of days. It can be a bit difficult though. Some are more obvious than others. I actually found it even harder as they got older with all the fur in the way.
“Both pictures of a buck, the one on the left is actual the one on the right is marked in red to make it a little easier to see. There is a little bit of a gap between the penile opening and the anus. This will not be present in the newborn doe.”
“This is a doe. The anus and vent will be touching.”
(
http://madhatterrabbits.wordpress.com/2013/01/03/sexing-your-rabbit/)
Weaning usually happens between 5-8 weeks. I like to keep them with mom til 8 weeks if possible, as long as she is tolerating them well. If she is getting fed up with them sooner and starts to nip or bite them, you may have to separate them from mom before 8 weeks, though it would be good if you could still return them to mom just for nursing if she will tolerate it, until they are 8 weeks old. One good thing to have for her in the cage to get away from them pestering her, is a box or something she can hop up on to get away from them for a break.
When to separate the babies, or even mom from babies, depends if you have boys or girls, and how mom does with them in her cage. If you have two does(which you would need to be sure of) and mom is fine with them in her cage and weans them on her own, you may just be able to leave them together with her, until they are old enough to spay and bond. If mom starts getting irritated or fighting starts to occur, you would need to separate. If you have one or two bucks, separate them from mom at 8 weeks, and you may be fine to leave the babies together until 10-12 weeks. I separated mine at 12 weeks.
And ENJOY! Raising baby bunnies is a fun experience