It looks very much like a modified Carter Bros 1135 ZX/KX. Or it could be stock -- never seen a brush guard/roll cage like the one that is on it. Presuming I am incorrect, you can identify it as good as anyone and I won't have to beg you for a dozen more photos... Start here:
www.bmikarts.com
Single seat karts all start with a "1" and two passenger karts start with a "2".
Here's my guess:
EDIT: Part number 27 "G314 Axle 3/4" x 38 1⁄4" is probably correct if the 1135 is your kart. So you might be off by 1/4"
Anything is possible in regards to finding an
exact replacement. Carter Brothers karts are very common...
However, non-matching off-the-shelf parts, like the one I linked in post #4, are why we have local machine shops, usually hidden away in the industrial side of town, to make 'em fit. You could have it shortened, threaded (more threads if needed) and broached (for a keyway), etc.
Otherwise ... you have some work ahead of you to measure yours for the proper specs you need and get a custom one from BMI:
www.bmikarts.com