Do Whatever You Find Easiest/Most Comfortable
I know this probably isn't very helpful of an answer by itself, but I feel like it is important to mention. There is no one right way to do answer this question.
One of the best things about RPGs with your SO: You're not going to judge each other. You're not going to hold each other to unfair standards. If you're learning together, you're going to be able to be flexible. If you try running a published adventure and it doesn't work, it's not a big deal: just try another method. You can (hopefully) communicate really well about what is and isn't working and what is and isn't fun for both of you.
These things being said, I've outlined some of my recommendations based on personal experience below.
One DM, One Party
In my opinion, the best way to go about 1-on-1 play is to have one person play the DM and one person play the party. This is what my fiance and I do; and it works very well for us. We both love RPGs and with this 1-on-1 style of play allows us both to get what we want out of the game. We are about to start two new campaigns: an AD&D 2E campaign run by her, and a D&D 5E campaign run by me. This does require one person to play 4-6 characters, which may not be ideal for your situation, but it requires minimum modification of the published material. One thing that may worry you with this method are that one (new) player has to create 4-6 PCs. This can be very overwhelming, but there are a few solutions to this problem:
- Use pre-generated (pregen) PCs for the first few levels. There are pregens in every level for every core class in the Core Rulebook and they can be found online, here.
- Each of you build a couple of the PCs in the party mechanically. Obviously, the person playing the party will need to come up with the backgrounds for the characters individually and the party background but this can be a good way for both of you to get experience with character creation in the system.
There are also ways to simplify your experience as you're learning such as only playing with the basic rules included in the starter set and limiting your content to the Core Rulebook material.
Don't Run Written Material
If the above solution doesn't interest you or SO, another option would be to run a single Hero/Heroine adventure where the player is the sole PC of the campaign. Obviously encounters would need to be appropriately balanced and if the PC isn't a healing class, some form of healing will need to be available but it is definitely doable. I would definitely recommend looking at some published material for an idea of how adventures usually go in the Pathfinder mythos but you don't need to be bound by the written encounters or setting. This would allow the DM to specifically tailor the adventure to the character's strengths and weaknesses and possibly help assuage holes that would normally be filled by other PCs. For example, only rogues can use Disable Device on magical locks/traps. If your PC isn't a rogue, don't include these in bulk in your story.This also may be more work than you feel capable of doing successfully and may not be the best for you since you described a desire to "ease in" to RPGs but I think it has a place in this answer.
Redesigning the Written Encounters
If you do decide to run a published adventure you will need to redesign the encounters. The Gamemastery Guide has rules on designing encounters which you can use as your guide to rebalance the encounters, but they may be overly complex for your needs. Some people may disagree with me, but I would say that a simple enough method to rebalance the encounters for a single PC would be to have one monster per PC/NPC in the fight. This brings me to my next point: the APs that I have played (Shattered Star & Reign of Winter) have multiple NPCs who would agree to join the party for some (if not all) of the adventure. You can use this to your advantage to provide more bodies for the monsters to hit when you feel that encounter theme/style/setting requires there to be multiple monsters. Additionally, your PC is free to hire hirelings as red shirts to soak some damage. In any case where you have a single PC, be sure to have a way of filling the holes (such as magical healing or an ability to open locked doors/chests).
I don't think you will readily find an Adventure Path that suits your needs due to the nature of Pathfinder's Adventure Paths. You may be able to find some modules (especially if you look at third party publishers as well) that were written for 1 player but I don't know of any off the top of my head.
I have played Dragon's Demand and I can say that you may be able to make it work for a single player. Without spoiling too many things: your PC starts off in a town where the DM could easily have an NPC offer to travel with them. Additionally, a certain class gets a large boost in gear right near the very beginning (whoever DMs can look this up, I don't want to spoil it) which may help to account for there only being one PC.
As a side note (mainly because it's simply interesting information) there are some older modules written for a single PC. Specifically what comes to mind are the AD&D 2E modules: Wizard's Challenge, Fighter's Challenge, Thief's Challenge, and Cleric's Challenge. I'm not advocating for you to get these and try to upgrade them to Pathfinder, I am merely including them to prove that there have been single PC adventures written in the past, so you may be able to find some now.