4E is "combat heavy" in the rules-explanation of the player's handbook, it is true. Indeed, it goes to great lengths to explain the details of the combat rules, because it has taken great pains to create a tactical miniatures game out of the combat system.
What they've done for the non-combat system is return to the very old-school idea of roleplaying minus a mechanic.
Instead of having your storytelling be restricted by a game mechanic, the non-combat portion of the game is very loosely structured around the skill system. The DMG explains about skill tests, and some other non-combat types of encounters.
But mostly it is a return to the original AD&D style of roleplaying, where the game mechanics themselves are concerned about the combat but the actual rules don't concern themselves with the non-combat aspects of storytelling. You've got just enough of a loose system of skills to control the action, but mostly what you've got left is the classic social contract between the GM and the players, working together to tell a good story together.
It is no longer about formulas, sheets of rules, and metagaming the non-combat portion of the game. It is about as old-school as you can get.
Or, as liberating as you can get! (they really do go to great pains to explain how they've adopted the "just say yes to players' ideas" mentality).
That is why there are not page after page of rules in the DMG. They've done away with them. They've got explanations, and suggestions, and advice, but not rules and mechanics and things that are going to bind you up, tie your hands, and hold you down.
So what's left if your daughter doesn't like combat?
Everything! Whatever the two of you can come up with! Whatever she can create! Whatever she wants, you can facilitate!
And thankfully, you won't be restricted by an overly cumbersome set of non-combat storytelling rules that keep telling her what she *can't* do, instead of encouraging her to explore the limits of what she *can* do in your shared world.