Associating the curl of a magnetic field with rate of change of electric field, and the curl of an electric field with the rate of change of a magnetic field, is extremely useful, but not necessary.
[Note: the time derivative of the electric field does not cause a magnetic field, it causes the curl of a magnetic field, which is a big difference.]
In the Jefimenko formulation of electromagnetism, the electric and magnetic fields at $(\vec r, t)$ are entirely caused by charges, currents, and their time derivatives...all at positions $\vec r'$ consistent with the retarded time:
$$ t_r = t - \frac{|\vec r-\vec r'|}c$$
There is no need to consider the state of the electric field when computing the magnetic field (and vice versa).
With that view point, a magnetic field some distance from a dipole, looks like a dipole field provided:
$$ \frac{|\vec r-\vec r'|} c < t-t_r $$
Moreover, if you do consider the standard formulation with Maxwell's equations, it's important to consider what part of the field is radiative, and what is near-field. The dipole (magnetic) field of a bar magnet, $\vec m$:
$$ \vec B(\vec r) =\frac{\mu_0}{4\pi}
\big[
\frac{3\hat r(\hat r\cdot\vec m) -\vec m}{r^3}
\big]$$
falls as $1/r^3$. The energy falls as $1/r^6$, and is not radiative.
