A few suggestions/observations from my (allegedly subjective) experience.
- Kids like pets, and pets make good tag-along NPCs. "Mundane" animals work, but unicorns that can heal, pegasi that can fly, bears that can share their strength, eagles that give you superior vision, owls that can talk and give wise advice, etc. have been huge hits in my games. Without intention of stereotyping, this may be particularly true with your 7y/o niece.
- Kids like challenges they can 1) relate to, and 2) contribute in some ways, no matter how small. These challenges don't need to be combat-oriented, or even pose a significant threat, all things considered. By "relate to" I don't necessarily mean real life, but their experience and knowledge of pop-culture, computer games, TV shows etc. At these ages, gender difference and 2 year gap can be significant. Or it may not be. But be prepared for them to relate to different things.
- Some kids mostly want, for lack of better words, for you to take them on a tour. They'll go to the next valley just to see what's there, and then leave for the next mountain. This has not been true with all my kids, but especially since you'll have one-on-one time with them, expect this as a possibility.
- Keep spells known to a very small, very manageable list. Forget about prepared spellcasters. If need be, give new spells as rewards.
- Some really enjoy the awesome!!! factor. Some are more modest. But in my experience, narrating how difficult and significant what they just accomplished was, is very rewarding for them.
I'm sure there's more. That's what I can think of right now.
Also, there are a few RPG specifically created for young players. They are worth looking into, and I'm betting they will have really good advice on DMing for kids.
[edit] Oftentimes, little things experienced adult players would find trivial are awesome for kids. I have in mind a Star Wars game where my son's character ability to kip-up as a free action allowed him to reach his ship and close the door before the bad guy. Of all things that happened in that game, that's what he remembers as a defining moment. In other words, don't be afraid to add little details, even if they sound/feel trivial. They may very well become memorable moments for them.