Hello! Congratulations on growing your first daughter. It bringing you to the character screen then the intro scene marks the end of a playthrough... Mushroom Musume is meant to be played through multiple times, so you can try to grow different types of mushroom (if you haven't looked through it yet, be sure to check out your Mushroom Almanac on the main screen to see what you've found so far!).
Different daughters have unique abilities and can sometimes make interesting choices in events, and there's more events in the game than any one daughter could see!