This is actually a common feeling in people with only one rabbit.
Yes, your rabbit might be feeling some separation issues due to being removed from his littermates recently, and also because he is quite young. However, your rabbit is now bonding to you and enjoying your companionship. Rabbits do wonderfully as “single” pets, especially because their schedules mesh so well with ours. While you’re at work, your rabbit is most likely sleeping anyway! Rabbits are most active in the morning and later in the evening, which are great times for you to spend with Peanut anyway. As long as you are spending time with him and allowing him to get adequate exercise and mental stimulation, I’m sure he’s doing fine!
I wouldn’t consider getting another bunny until you have bonded with this little guy and he is old enough to be neutered, anyway. Most members here recommend waiting a year or two to spend with your rabbit before introducing another one into the mix. It takes quite a while to truly bond with a rabbit and earn their trust, so I would make the most of the time you have with the rabbit you have and not worry about getting him a friend until you both are truly ready.
If you’re concerned about your rabbit when you leave, get him a stuffed friend! There are rabbit look-alike stuffed toys, or just give him a teddy bear to snuggle (provided that he doesn’t chew it to pieces). Also, make sure he has plenty of chew toys, like willow sticks or willow balls, toilet paper tubes, or plastic jars (like clean peanut butter jars) with rocks inside to roll around. A digging box or phone book is also another great option.
I wouldn’t worry too much about your rabbit being lonely; although rabbits do enjoy each others’ company, it isn’t a necessity. Rabbits do well on their own as long as they have a loving owner and are provided with a lot of entertainment!