Hi
The buggy looks like a custom or homemade item, and it looks like a good build although others members may be able to add further insight.
I would suggest that you build the buggy up and adjust for size at home, which means you will be ready to go when you arrive at the flying zone.
One thing I like about the design of your buggy is the luggage rack, I haven't thought of this addition before, it makes sense., looks really functional and would be a handy place to store kites and stakes close to hand.
I believe the majority of mass-produced buggies (if there ever was a such thing) are supplied with rims that look pretty much like this:
Hub
These can come with 2 standard sized bearings & bolt sizes, of either 12mm or 20 mm bolts, the 20mm is normally used for bigfoot / larger tyres (race buggies) or on buggies used for ariel tricks, sorry I do not know the bearing specs.
The rims pictured look to be different to the commercially used rims, but they should be able to take the load.
I would suggest that you remove the bearings for inspection before you think about buying new, if they have a rubber shield you can disassemble them and inspect for damage, normally they just need a good clean. please see below a link on how skateboarders refurbish bearings.
Strip, Clean & Rebuild
If your bearings have no surface damage and are cleaned, lubricated and rebuilt, they should be fit for loads more miles and smiles.
Just be careful not to damage the rubber Shields when / if you strip the bearings down, any damage to the shields will leave a gap for dirt and grit to get into the bearings in the future.
I don't know where on earth you are, I am in the UK and these are the suppliers I have used for bearings and tyres before:
Bearings
Hubs & Tyres
Hope the above helps, good luck and enjoy!