Keeping aside its stability and considering only their structure and structural formula, is peroxynitrous acid an isomer of nitric acid?
Yes.
It seems that peroxynitrous acid is a very, very unstable compound and I hardly doubt that it has been synthesised in pure, stable form. This video shows the preparation of peroxynitrous acid but it readily converts into nitric acid and so the peroxynitrous acid yield is very poor.
Indeed, it is impossible to isolate peroxynitrous acid $\left(\ce{ONOOH}\right)$ in aqueous solution, due to the rapid decomposition to nitric acid. The yield is not just poor, it is zero.
However, the conjugate base of peroxynitrous acid, peroxynitrite $\left(\ce{ONOO^-}\right)$, happens to be extremely stable. (Apropos the question, peroxynitrite is an isomer of nitrate.) So, as long as a synthetic approach is devised that keeps the product strictly in its anionic/alkaline form, one can actually produce peroxynitrite solutions and salts and work with them in experiments. In fact, I synthesized sodium peroxynitrite solutions myself as part of my Ph.D. research. You can read about the procedure in Section 4.2.4 of my thesis (free for download). A short literature review of various $\ce{ONOO-}$ synthesis methods is also included there.
Briefly, I loaded aqueous solutions of (1) $\ce{NaNO2}$, (2) $\ce{H2O2}$ plus $\ce{HCl}$, and (3) $\ce{NaOH}$ into syringes fitted onto a syringe pump. I then connected the syringes to a tubing network that first mixed the acidified $\ce{H2O2}$ with the $\ce{NaNO2}$, forming $\ce{ONOOH}$, and then quickly mixed the product solution with the $\ce{NaOH}$. The alkali "caught" the $\ce{ONOOH}$ while a significant concentration still remained, providing a bright yellow solution of alkaline peroxynitrite. After decomposing residual $\ce{H2O2}$ by treatment with $\ce{MnO2}$, these solutions held their concentrations for a couple of years when stored at $-80\,^\circ\mathrm C$.
