Most Glocks are substantially more accurate than some shooters give them credit for. That said, it has been my experience the .40 cal Glocks are the least accurate by a wide margin.
9mm and .45 Glocks are very accurate if you can master the trigger, including follow through.
As an example, years ago when I was a state police firearms instructor, I made a point of doing a 50 yard demo from the roll over prone, and would place all the rounds in the head of a standard B27 silhouette with the issued .45 Glock 21. I could not do that today, accuracy wise, but the gun can.
Ringing the 100 yard plates with my G34 9mm is no problem.
I have only fondled the 43 and have not shot one yet. I cannot comment on their accuracy potential, but if they are similar in accuracy to a 26 or 19, you will have zero problems whacking rabbits/small game well beyond 25 yards.
My partner at work and one of our detective sergeants both just picked up 43s. I will see what they can do the next range day.
I like your idea of a 43 as a kit gun. Talk about light and small!