This is very close to a classic Japanese miso soup. The broth, or dashi, is traditionally made with kombu or kelp, sometimes dried mushroom, and dried fish flakes or bonito. You can omit the fish flakes and still have a nice flavorful soup, although not quite as rich a taste.
Lighter misos work better in hot weather, and darker misos make a richer soup for colder weather. The miso is traditionally added right before serving for best taste and nutrition.
For best taste, try to adding miso to the point that the soup just begins to taste salty. That will bring out the full, sweet taste of the miso and broth to best advantage. Start with a lesser amount and add more until you get a feel for how salty you like it.
The wakame needs to be soaked in warm water for about 10 minutes before chopping and using. It expands quite a bit on soaking, so start with less than you think you will need. (I have been making this soup for years and I still end up soaking 2-3 times as much as I need.)
You can vary the vegetables to good effect - for example, a bit of grated zucchini works well.
To make the broth - add the kombu and dried mushroom to the water, and bring just barely to a boil on a medium flame. When it just starts to boil, turn off the flame and add the fish flakes. Let the broth sit about a minute then drain. You can keep the kombu to use again, and chop up the dried mushroom to add back. Discard the used fish flakes. Add the carrot, wakame and tofu to the broth, and heat over low flame for a few minutes until they are warmed through. Then turn off the flame.
In a bowl, mix the miso and a little bit of the broth, and mash the miso with a fork to a loose paste. Add to the soup, stir, and taste. Repeat until you get it to the strength you want. Serve each bowl garnished with scallions. This recipe makes about 4 servings.