Unless that caster plate ends up underneath the 2x4 when bracket is flipped down for use, all the load is passing through the screw hardware on the side of the 2x4 - a bad design for moving heavy loads across potentially bumpy terrain.
I made a tractor for our old rabbit and it used the same size pneumatic tires - PITA to move around on grass with that small of a diameter wheel and a decent weight load.
A design using larger diameter wheels, such as bicycle tires would be a better choice IMO, I’ve got a garden cart with bike tires and that thing smoothly moves heavy loads across my property.
If you search the internet you’ll see some coop wheel designs that are mounted on a steel lever, that swings to engage wheels and lever handle locks into position. IMO this is a good design choice for mounting bike wheels as the connection and pivot can be made to be heavy duty.
Good luck!