Well first off, let her know you've never refereed before, so you might get some things wrong.
Second, figure out what kind of movies, books, video games, etc she likes. Doesshe like the hack and slash? Does she like the roleplaying and social interaction?
There are a lot of awesome adventure ideas that you can't do with (or would be difficult with) a whole party.
Third, you don't want to make her too high level because she will get bogged down.You don't want her too low-level because she'll die right away
Third level would be a good choice, probably a Fighter or Rogue (3E, I dunno about 4E). Spells are a bit complicated. Make up a few pregenerated characters and let her choose one. If it dies she can grab another one and approach it different way. Let her know that in a regular game she'd make up her own character from scratch.
Fourth, short play sessions. Don't bog her down with an 8-hour standard game. Right after lunch is a great choice too, because you're both carbed up and thinking straight, and pleasant, and not tired like you would be after breakfast and dinner. Likewise, pick a day you're both in a good mood. First impressions and all.
Fifth, regardless of what else happens, there must be a happy ending. Again, first impressions. People
remember their happiness level of their experiences based strongly on the ending, or the "punch line". This may be hard to do though, and I haven't experimented with it yet.
Sixth, provide some direction, but make it obvious that she can make her own decisions. She may not follow the plot anything like you expect, and as a new referee you'll have a little trouble adapting on the fly. Be patient and relax. This is also why being rested and well-fed helps.
I'd suggest a town-style mystery where the whole town is hiding some secret, and they just hope the stranger who rides in doesn't get involved. Maybe a lawman of some type.
Or a prisoner escape, finding lame and improvised equipment on the way, through some caves and such. I believe the old adventure was called Scourge of the Slave Lords.