I think your construction is correct, but a hemisphere with the usual outward normal framing is also a framed nullcobordism of $S^1$ with the outward normal framing. Which is good, since the Pontryagin--Thom construction gives you a bijection from cobordism classes of framed submanifolds of dimension $1$ in $\mathbb{R}^2$ to the unstable homotopy group $\pi_2(S^1)$ which vanishes.