Definitely. A small dog will need a smaller bed than a bigger dog. Also, small dogs can sleep in big beds, but big dogs can't sleep in small beds! Bigger dogs also need more support, since they weigh more, so it's good to get a better quality bed for big dogs.
Additionally, you need to think about if your dog has any bone or joint problems. If this is the case, then they'll need more padding on their bed, or you could even buy a memory foam bed for them. This will cost more money, but it's worth it if it will help your dog lead a happier life.