How to determine the order of a reaction with not a commensurate rate equation
To be honest with you, the term "order of reaction" is not an exact term. If I want to pull out the rigorous kinetician out of the closet, I'd say that only elementary reactions have orders, and we have first or second (or zero or maybe third) order reactions only, and they are obvious to spot. 

What you have is not an elemental reaction, but an overall - somewhat empirical - net reaction rate for a complex mechanism. I personally do not like to talk about orders of non-elementary reactions, but some authors do this. In this context, I'd say your reaction is first order in $\ce{N_2O}$, simply because you have concentration squared divided by approximately concentration. Note that if $\ce{[N_2O]}$ is sufficiently large (so the $1$ in the denominator is negligible), the equation becomes $-r =\ce{\frac{k_1 [N_2O]^2}{k_2 [N_2O]} = k' [N_2O]}$, so in high concentration limit the unimolecular approximation becomes exact.