The rates of the F-18(p, alpha) O-15 and F-18(p, gamma) Ne-19 reactions in astrophysical environments depend on the properties of Ne-19 levels above the F-18+p threshold. There are at least eight levels in the mirror nucleus F-19 for which analogs have not been observed in Ne-19 in the excitation energy range E-x=6.4-7.6 MeV. These levels may significantly enhance the F-18+p reaction rates, and thus we have made a search for these levels by measuring the H-1(F-18,p) F-18 excitation function over the energy range E-c.m.=0.3-1.3 MeV. We have identified and measured the properties of a newly observed level at E-x=7.420 +/- 0.014 MeV, which is most likely the mirror to the J(pi) = 7/2 + F-19 level at 7.56 MeV. We have additionally found a significant discrepancy with a recent compilation for the properties of a Ne-19 state at E-x=7.5 MeV and set upper limits on the proton widths of missing levels.