Using time-resolved small angle neutron scattering, we have measured the wave-number-dependent structure factor S(q) of monodisperse nanoemulsions that aggregate and gel after we suddenly turn on a strong, short-range, slippery attraction between the droplets. At high q, peaks in S(q) appear as dense clusters of droplets form, and S(q) increases strongly toward low q, as these dense clusters become locked into a rigid gel network, despite the fluidity of the films between the droplets. The long-time high-q structure of nanoemulsion gels formed by slippery diffusion-limited cluster aggregation is universal in shape and remarkably independent of the droplet volume fraction, phi.