It's a little tough to tell from that one photo but I am seeing that you have an inner wheel bearing that's larger than the outer bearing. That is typical on
today's axles rated at up to 3500#. Most of the 2000# class axles will use the same size bearings (either 1" or 1-1/16") as both inner and outer bearings. Check the inner diameter of the inner race of the inner bearing. Did I get that right?
That is, the inner diameter of the larger bearing. Is it 1-3/8"? If so you are probably good to go.
I don't know how old your trailer is, it appears to have a drop axle so that it will sit a little lower than it would with a straight axle. It also seems to have of a set of leaf springs more like those used on a car, rather than standard trailer leaf springs which are generally quite a bit shorter in length. I would assume that it will ride smoothly, but it might benefit from a set of shocks if the trailer bounces around too much. Also, you might be able to mount the axle over the springs rather than under them to lower the whole rig if you wish, detailed pictures would help.
Maybe a good way to check out the whole chassis is to load it up with some stuff to where it weighs about 1200# and see how the trailer handles things. With the trailer empty you could weigh each wheel load with a bathroom scale. Ditto the tongue weight. Add them up an it would be pretty close to the empty trailer weight. Weigh items of "freight" with the bathroom scale and put 'em in the trailer, keep your hitch weight at 10-15% of the total trailer weight.