You will be fine, if it starts downshifting at the sight of the slightest hill, turn off OD. When I tow my jeep with my truck, I run with OD off if I am under 70, I turn OD on if I am doing about 70-75 on flat surface. But that is about 6,000lbs with trailer over your 1,000lbs so you will be fine. Just make sure you check your transmission fluid before you go and load the ATV nose first to keep the weight towards the tongue to prevent trailer sway.
1996 XJ on 36" TSLs, 4", locked F/R, stretched