Might be easier to expand out the arguments so you can differentiate w.r.t. each one individually?
julia> dfdx(x,y) = ForwardDiff.derivative(x->test_fun((x,y)),x)
julia> df2dxy(x,y) = ForwardDiff.derivative(y->dfdx(x,y),y)
The error occurs because test_fun has a vector/array argument, while evaluating ForwardDiff.jacobian at x[1] expects a function with a scalar argument.