>>/4310/
> is it possible to learn cats land vehicle proficiency?
As far as I'm concerned you don't need proficiency to drive this cart.
From what I understand, it just adds the proficiency bonus to checks in "difficult circumstances".
So there's a chance of getting stuck in a rut and lose an hour, there's a chance to break an axel, wheel, or yoke, a horse may come loose, but horses are very tame. If she has a proficiency like that then any rolls would benefit from that. I wasn't aware she had that buy I'll take your word for it if she does.
In general proficiencies will help but you don't need it to use something, not in my game anyway.
So to answer your question, you won't gain proficiency in the course of this quest unless you level up and use that opportunity to choose that proficiency. You won't strictly need it though. I recommend swapping with cat when you hit rough terrain if it occurs.
Other hazards that may not be included in "mounts and vehicles" proficiency would be making a broken part (tinkering) though you could repair or replace it.
Cat would be better at chasing down a loose horse (animal handling), packing to get more in it, but her animal handling skill is also useful for treatment of the horses, driving them harder or longer, etc so it's good for her to drive for that reason too.
Formation is good, if you are ambushed they may come from any direction though.
This should be easier than Oregon Trail. No one's going to steal your clothes, food or horses at night. Assume that there's a spare part for most things on board but not an infinite number of them. Rolling a couple 1's in a row could be a bad day.
[1d20=1] "HORSE 1 GETS DYSENTERY."
You're lucky we're not playing Oregon trail.