Hi there Summer's mum/dad, welcome to the forum :wave:
It sounds like Summer is just producing too many caecotropes. Excess caecotropes are commonly caused by diet or stress, but I believe they can also be caused by using inappropriate antibiotics. Obviously this isn't the case with Summer.
As lovelybun has said, a good place to start is her diet. I should point out that I have only ever had adult bunnies, and all my information is about them, but there are many young bunny owners on the forum who will hopefully come along to give age-specific advice.
In an adult bunny, I would first reduce the pellets. However, I'm wary of recommending this as Summer is younger - please wait for someone with experience in young bunnies to confirm this, and you can always ring your vet for advice
Adult bunnies only need an eggcup full of pellets, all the rest should be lots and lots of hay! You have done absolutely the right thing in getting alfalfa hay as it contains higher levels of calcium needed for young buns, as Summer gets older you can change it to timothy.
The other factor is stress. As you have only had her a few days, and she is so young, she is likely to be a bit stressed by all the changes. If stress is the cause, it should settle down itself as she becomes used to her new home. As said above, if you notice any changes in Summer's diet, drinking, behaviour or poo, you should take her to the vet urgently.