Okay, after much troublesome digging through the source code I have found a way to get the permutation. I have included it as a function below, should anyone else need something like this.
function getdofperm(dh::DofHandler)
p = fill(0, getnnodes(dh.grid))
for cell in CellIterator(dh)
_celldofs = celldofs(cell)
for (i,node) in enumerate(getnodes(cell))
p[node] = _celldofs[i]
end
end
return p
end