We present Spitzer IRS 5-14{mu}m spectra and 16{mu}m and 22{mu}m photometry of the T2.5 companion to the ~300Myr old G0V star HN Peg. We incorporate previous 0.8-5{mu}m observations to obtain the most comprehensive spectral energy distribution (SED) of an intermediate-gravity L/T-transition dwarf that, together with an accurate Gaia EDR3 parallax of the primary, enables us to derive precise fundamental parameters. We find that young (~0.1-0.3Gyr) early-T dwarfs on average have ~140K lower effective temperatures, ~20% larger radii, and similar bolometric luminosities compared to >~1Gyr old field dwarfs with similar spectral types. Our accurate infrared spectrophotometry offers new detail at wavelengths where the dominant carbon-bearing molecules have their strongest transitions: at 3.4{mu}m for methane and at 4.6{mu}m for carbon monoxide. We assess the performance of various widely available photospheric models and find that models with condensates and/or clouds better reproduce the full SED of this moderately young early-T dwarf. However, cloud-free models incorporating a more general convective instability treatment reproduce at least the low-resolution near-infrared spectrum similarly well. Our analysis of R~2300 J-band spectra shows that the near-infrared potassium absorption lines in HN Peg B have similar strengths to those seen in both younger and older T2-T3 dwarfs. We conclude that while alkali lines are well established as surface gravity indicators for L-type or warmer stars, they are insensitive to surface gravity in early-T dwarfs.