Nineteen of ~40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. We present results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on ~18400 long-cadence observations per star (and ~150000 short-cadence observations for two stars) are presented. None of the stars shows the recently discovered `period-doubling' effect seen in Blazhko variables; however, one star has been found to pulsate simultaneously in the fundamental and second overtone modes with a period ratio P_2/P_0 ~0.59305, similar to the double-mode star V350~Lyr discovered previously. Period change rates and high precision periods are derived from O-C diagrams spanning, in some cases, over 100 years. Extant Fourier correlations by Kovacs, Jurcsik et al. (with minor transformations from the V- to the Kp passband) have been used to derive underlying physical characteristics for all the stars. This procedure seems to be validated through comparisons of the Kepler variables with galactic and LMC field RR Lyr stars and with RR Lyr stars in galactic and LMC globular clusters. The most metal-poor star in the sample has [Fe/H]_ZW = -2.25 dex; fourteen of the stars have metallicities between -1.35 and -2.02 dex; and the four lowest amplitude stars are found to be quite metal-rich with [Fe/H]_ZW between -0.47 and -0.86 dex. The metal-rich stars also appear to have the lowest luminosities and masses. Pulsational luminosities and masses are systematically smaller than values based on stellar evolution models (similar to the Cepheid mass-discrepancy problem). Finally, the Fourier parameters are compared with theoretical values derived using the Warsaw convective hydrodynamics code.