Which column properties? To which columns? Some do get copied over just fine.
If you are willing to utilize clipboard scripting index does provide quite simple example of copying column properties using JSL
Names Default To Here(1);
dt = Open("$SAMPLE_DATA/Tiretread.jmp");
dt << Copy Column Properties({:MODULUS, :ELONG});
dt2 = New Table("test it",
New Column("T1", numeric, continuous),
New Column("T2", numeric, continuous),
New Column("T3", numeric, continuous),
Add Rows(10)
);
dt2 << Paste Column Properties({:T1, :T3});
-Jarmo