I see this question arise frequently and thought I would share my experiences over the years to help you make a good decision. This is something that should be well thought out and knowing what you may face could help you make a good choice.
First may I tell you that getting two pups at the same time is rarely a good decision. Most reputable breeders would never give you this option because it poses many great difficulties. Raising a puppy can be a full time job if you are a dedicated parent who follows a good structured routine. Pups have many new things to learn and that becomes your job once they enter the home. They need to learn the appropriate potty place, how to walk on lead, how to respond to different sounds and smells. They need to learn about new environments, acceptable behavior when meeting other dogs and people. How to be groomed and bathed. They have many trips to the vet. They learn about crates, acceptable items to chew on and basic commands. This is most challenging for the most experienced of owners. Typically not a good choice for most people.
I have generally recommended that people wait until their pup is at least a year old before adding another. This gives you time to attend to the basic training of your first dog and help him be well on his way to being a solid companion before adding another. You will learn good information during this year that will hopefully help you if you decide to add another pup later. It is most important that your dog be well socialized and accepting of other dogs before making this decision.
One must also consider the reasons for adding another dog. I often hear "my doggie needs a pal" I can assure you this is rarely true. While your dog may be playful and enjoy other dogs it doesnt necessarily mean that he "wants" another dog to live with. Heck, dogs dont even think in those terms. Playtime with other can be arranged by a dedicated owner so your dog has this outlet. Many also think that if their dog has a "buddy" they will live harmoniously and play all the time. They think their dog will never be lonely and will not require as much attention if they have another dog. This may be true in some ways but adding another dog also changes the dynamics of ones life drastically.
If you are still in "training" mode with your first dog adding a second makes it difficult to know who the offending dog is with potty accidents, chewed items, etc. It makes attention and focus difficult to achieve with either dog as they develop a bond with one another. Time must be taken with each dog separately to train them. Well trained dogs offer a great role model to young dogs.
One must have a basic understanding of dog behavior. Frequently I am contacted from people that have fighting corgis. This generally happens because the owners have not been aware of all the warning signs the dogs have offered. Corgis are often quite possessive and pushy and can issues over things such as food, treats and possessiveness of their owners. They can be noise reactive, protective of their space and often have difficulty with doorways. Possessive and over excited dogs can be most difficult to control. One must be most aware of these issues and stay on top of them "before" a problem breaks out. Dogs that have been fighting for a time can rarely be taught to live harmoniously.
Know that expenses will double by having two dogs. Veterinary costs have risen drastically over the past few years. Please consider this before adding to your home. Many are shocked when they learn the cost of vaccinations, spay/neuter, parasite control and quality food. You also have supplies such as collars, leads, toys, crates, beds, etc.
Consider what stage in life you are in. Are you a college student who lives alone? Are you in a roommate situation with other animals? Do you live with a significant other? Are you in an apartment? Planning on getting married soon? Thinking of children? All of these factors must be considered as these indicate big changes in your life to come in near future. This also can cause great difficulty while raising young dogs. I get many calls in rescue because folks are moving, they have a baby on the way or they can no longer afford to keep their dog because of new and unexpected expenses.
Many think that having two dogs will offer an outlet for exercise. This is surely true but one must also consider that "controlled" exercise is a great part of training a dog. They must learn how to be mindful of the humans in their life and be responsive when called upon. This is most difficult to achieve with several dogs that are in all their glory playing. In no way would this diminish the time you need to spend with each dog. Walking one out of control young dog is tricky. Two is near impossible. Each dog will need singular training and bonding time with their owners to be well behaved companions.
Temperament is a great consideration when adding a new dog. I generally recommend the male/female combo as they seem to naturally get along. Two neutered boys is my next choice. Two girls can be a poor choice. This combo is one that proves most difficult for many. The girls are pretty unforgiving and frequently compete for top dog. Most of all compatible temeraments are most important. A knowledgeable breeder will be most helpful in this area. A well balanced pup or dog is always the best choice. Long time kennel dogs, isolated dogs and fearful dogs make life more problematic for you and your dog. I always encourage people to avoid the most gregarious pup in a litter as well as one that does not choose to interact. Moderation is the ticket here as generally these pups are most adaptable.
Certainly there are many other things to consider. Hopefully this will help you think a bit deeper before adding a second dog. I am all for it, I currently have five and have had as many as eight. I also know how much is involved and have dedicated myself to achieving a harmonious living situation.