Practice driving the truck and trailer. Go to a Walmart parking lot (or any big shopping center lot) and practice driving and turning. To practice backing up the trailer, use street cones and back between them. The longer the trailer the easier it will be to back up.
LOL I learned to back our trailer up backing down the loooong driveway at my friend's dairy picking up calves. I also learned more backing up at a Fair where they did some screwy camping thing for one year. You had to back in but they didn't tell anyone and had no signs up, so I had to back out a long driveway, back around a corner to the left, then back around another corner to the right, then pull out and back around another corner to back down the driveway back to the campground! Just practice and you will do fine.
Oh yes, stop for gas at truck stops since they usually have a lot of room to maneuver.
As far as moving the goats, just make sure that you have pens ready for them to be unloaded into. If you don't have pens there already, buy portable panels, go to the property, set them up before you bring the livestock in. Make sure you have feeders and water containers ready to fill. BRING A HOSE WITH YOU. There is nothing so annoying as to arrive at the pens and have no way to get water to the animals. Ask me how I know.


This is why I make sure to carry a hose with me when transporting livestock. Also, if you can get hold of some 5 gallon Sparkletts type bottles, carry those with you to water the animals during the drive. If your goats are still in milk, bring a portable stanchion and milking equipment. Stop at a truck stop and park in the back then you can milk on the road. Dump the milk if you have no way to strain and refrigerate it. Be prepared for the goats to yield less milk for several days after the trip due to stress. (Experience from transporting dairy goats to and from shows all over southern CA.)
Expect the worst and prepare for it. If you are prepared for everything, in my experience everything will go perfectly!