Yep, you need an inverter. If you do decide this is needed, check the forum. Most everyone has done this mod if the dry camp at all.
Watch your wire sizes. 120 watts AC may only be 1 amp AC but it is 10 amps on the DC (battery) side. We just went over all this just this week.
I recommend you look into a 600-1000 watt "pure" sine wave inverter. They are pricey but worth the money. The "modified" sine wave inverters are much cheaper but unreliable for computer use.
Wiring a 1000W Xantrex inverter ?
Read through this Thread
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW