I have done a lot of one-on-one roleplaying similar to what you are describing, and I think there are several different approaches. You can use some of these simultaneously or (with a bit of work) switch between them throughout a long campaign, but each is pretty much a stand alone technique that at least for me has made solo games work well.
Run Solo With a Tailored Campaign
You can carefully tailor the campaign to emphasize the character's strengths, avoid things that are impossible for the character, and hit their weaknesses only to present a challenge to be overcome creatively. Actually, I think that this is a good suggestion for just about any campaign no matter the party size, but it becomes both much easier and much more important when running solo with a standard character.
Done well, this is sufficient to let any character be the star of the story without a party. Think about many of the action movies with one clear hero that handles all the action by himself/herself or any of the similar video games where you play a single hero without backup. The tombraider series does this well.
Make the character powerful
A single 3rd level character will often be more powerful (though also more narrow) then three first level characters. So, if you want to play solo you can often take an adventure designed for a party of first level characters and run it with a 3rd or 4th level character. This doesn't quite always work, there are times when you really need a second set of hands, but it works a lot of the time, especially if the character either is of a highly versatile class or dips into a second class for breadth. It doesn't hurt to let them be on the high side of the wealth by level recommendations to make sure they are equipped for a wide array of possibilities.
Provide a party of henchmen
Done right, there is nothing wrong providing NPC party members. The problem is that when you have a full party to start with, it is very hard to do it right. There is a temptation for the DM to identify with the NPC party member and make it a DMPC and even start dipping into "Mary Sue" territory with reality warping around the DMPC to make them seem awesome. Even if the DM is scrupulous in avoiding that tempetation, there will be a tendency (at least in some groups) to assume that that NPC has special insight and give what they say too much weight.
But those problems are greatly reduced and the benefits of NPC party members are greatly enhanced when you have a very small group of PCs. The key is to make sure the limelight is on the player. This doesn't mean that the NPCs shouldn't be fully fleshed out characters with their own feelings and opinions, but it does mean that the PCs should be the ones calling the shots and getting most of the glory. This can actually be easier if the NPCs are fully developped characters, as long as they have a reason to defer to the PCs.
Dragon Age (the video game) did this very well. You wind up with a whole group of followers, each one is well fleshed out (at least if you bother to find out about them) and provoked enough they will leave or even attack you. But each one also has a reason that they follow you, obey you, and defer to your judgment. Zevran is alive because you spared him and he sees himself as owing you fealty. Leilana believes (perhaps rightly?) that she was ordered by her deity to obey you. Allistair is (at least at the start) explicitly hesitant to make decisions and somewhat submissive. They are all every bit as powerful as your character and arguably more experienced, but they each have a reason that they will defer to your character and obey (most) orders.
Its not necessary, but this is more believable and easier if the PCs are mechanically more powerful than the NPCs. This makes it hard for the NPCs to outshine the PCs except when the NPCs particular class skills are needed. If you want there can be something story wise or even mechanical, beyond just being higher level, about the PC that makes them the natural leader. Perhaps they were marked by fate itself, chosen by one of the pantheon, of a particular lineage (remember that in the late middle ages your lineage mattered a lot).
Let the players have multiple characters
I have heard of this working, but I have never seen it work in a solo campaign. I think it would work well on a tactically oriented game but less well if you want serious character development.
I have seen it work well with multiple players but normally when there was a reason that there characters would rarely be in the same place at the same time. (In a Vampire: The Masquerade game I have seen players each have a Vampire and also each have a ghoul or just servant that was active during the day...) If your sister wants to do hack and slash this could be perfect for her, but if she wants to deal with the motivations of her character this could be a distraction.