I’m very sorry you lost Pepper. Pneumonia is very serious and it can progress very quickly.
Rabbits can get pneumonia when a “bunny cold” goes down into the lungs, or they can get it post a choking incident, if they breathe in a piece of food (aspiration pneumonia). Aspiration pneumonia is as a rule caused by bacteria that normally lives in the mouth and throat, where they dont cause any harm.
If you are lucky, you can treat it successfully with antibiotics and supportive care, but the prognosis is often poor, especially when it’s a bacterial cold that has spread to the lungs.
It’s not possible to replace a pet with another pet, and whether you want to adopt another rabbit soon or wait is completely up to you. There is no shortage of rabbits in need of a good home.
You should clean out Pepper’s cage and wash all his things before taking in another bun, just in case what caused Pepper’s pneumonia was something potentially contagious. Vinegar and water is good for cleaning rabbit cages etc with. If you want to be extra thorough, you can use Virkon, a rabbit safe disinfectant that is very powerful against lots of microorganisms.