  Collisionless Dark Matter Only (DMO) structure formation simulations predict
that Dark Matter (DM) haloes are prolate in their centres and triaxial towards
their outskirts. The addition of gas condensation transforms the central DM
shape to be rounder and more oblate. It is not clear, however, whether such
shape transformations occur in `ultra-faint' dwarfs, which have extremely low
baryon fractions. We present the first study of the shape and velocity
anisotropy of ultra-faint dwarf galaxies that have gas mass fractions of
$f_{\rm gas}(r<R_{\rm half}) < 0.06$. These dwarfs are drawn from the
Engineering Dwarfs at Galaxy formation's Edge (EDGE) project, using high
resolution simulations that allow us to resolve DM halo shapes within the half
light radius ($\sim 100\,$pc). We show that gas-poor ultra-faints ($M_{\rm
200c} \leqslant 1.5\times10^9\,$M$_\odot$; $f_{\rm gas} < 10^{-5}$) retain
their pristine prolate DM halo shape even when gas, star formation and feedback
are included. This could provide a new and robust test of DM models. By
contrast, gas-rich ultra-faints ($M_{\rm 200c} > 3\times10^9\,$M$_\odot$;
$f_{\rm gas} > 10^{-4}$) become rounder and more oblate within $\sim 10$ half
light radii. Finally, we find that most of our simulated dwarfs have
significant radial velocity anisotropy that rises to $\tilde{\beta} > 0.5$ at
$R \gtrsim 3 R_{\rm half}$. The one exception is a dwarf that forms a rotating
gas/stellar disc because of a planar, major merger. Such strong anisotropy
should be taken into account when building mass models of gas-poor
ultra-faints.
