I have this generator, and no surging at idle. I agree with the prior poster that it sound like something is up with the carb. How long have you owned this generator? How often do you run it? How old is the gas that is in it? You could first try running a strong dose of seafoam to see if it can clean out the problem. Champion does recommend 30 minutes of running every 30 days to keep things fresh. If this is the first time you have run it, I'd put a fair amount of fuel in it, plug it into something that will generate a load(maybe your TT with the A/C on), and let it run for a few hours as break in.
I had a different issue, but can certainly attest to the fact that they have great customer service. I will also add that they have a network of supporting dealers for repairs that they don't mention on their website. They were able to refer me to a repair shop in my area who did my warranty repairs.
Dave
2016 F350 Lariat 4x4 FX4 SRW CC SB 6.7 Magnetic Metallic
2017 Forest River Cardinal 3850RL