I know there has been some other threads about how to play a game with a one LM and a one player but mine will be a bit different. I want to introduce my sister into the rolaplaying games. She is twelve and has no experience with any roleplaying games whatsoever. But she is very into fantastic literature and read the Hobbit and LOTR (thanks to me lol).

Basically I want to add an NPC to the game played by myself so the party will be of two characters. But I want more of a social game rather than a combat oriented one. So any ideas?

Does she want to play a hobbit?

I'd think a two-hobbit company would be a great excuse for wandering around Wilderland meeting people (since they'd be outsiders unfamiliar with the area), and since hobbits are relatively weak in combat, this approach might offer a good reason to avoid fight-heavy scenarios. The NPC hobbit could be a friendly social equal (á la Merry and Pippin) or a servant (á la Sam and Frodo), depending on how much interaction you want to play.

It is a good idea actually. Two hobbits like Merry and Pip looking for adventure and wandering around could be a nice place to start rather than an elf or a dwarf character.

Farinal,
Perhaps the characters are here to establish trade with the Dwarven toy market? Or to learn the toy-making craft?

The Hobbits might arrive with the idea of starting trade, but after a bit of playing they realize that it would be very expensive to ship all those toys back to the Shire? So instead the Hobbits learn to become toy makers themselves? They could always buy and have shipped certain parts that require Dwarven skill to make. A small cart with two or three crates might contain enough parts to keep a shop back in the Shire crafting toys for the next year or two.

So the campaign would mostly center around making friends with the Dwarves and finding one who is willing to teach the Hobbits the toy-making craft. You could use Tensen01's Dale Gazetteer as the general backdrop of the city. That would save you a lot of effort in creating NPC's, stores, etc.