Re-using breaker box?

Mel, that old box is wired incorrectly! The grounds are on the neutral bar and the common is not connected. I would by a new one.

Here is one Home Depot carries under $30:

www.homedepot.com/p/Square-D-QO-60-Amp-2-Space-4-Circuit-Outdoor-Main-Lug-Load-Center-with-Non-Metallic-Enclosure-and-Neutral-QO24L60NRNM/100174454

Feel free to email with questions.

mel if it were me I'd replace the box and populate it with new breakers.  But to address your question about the existing box you first need to figure out if the box has continuity with the buss bar that currently has the grounds connected.  If it does, then the grounds can remain connected to it, and you'll need to install an isolated (has an insulating layer to keep it from touching your breaker box) buss bar for the neutral wires.  If the existing buss bar does NOT have continuity with the box, then I'd install a buss bar that DOES contact the box, move the grounds to the new buss bar, and connect the neutral wires to the existing isolated buss bar.

Edit: you'll also need a jumper wire to connect those two main lugs together.  As it stands, only 1 breaker would be energized if you hooked it up without the jumper.

I'd still replace the old breaker(s) with new ones if you can find them.  Breakers can wear out, and they can be affected by exposure to the elements.  If it wasn't wired correctly to begin with, you have no idea what kind of torture those breakers might have been subjected to.  So in the end installing a SquareD box with widely available breakers might not be much more expensive than just buying new breakers for the existing box.

If you notice the pic, the neutral bus was isolated but it has a green screw right in the middle that bonds it to the actual housing which is correct if you consider it the first means of disconnect. The only problem would be that if your source of power is coming from a ground fault then you would have 2 different neutral bond sources which would cause nuisance trips. I would say if you know your power source is bonded correctly then I would not bond the neutrals and grounds at the camper.