Yes, you could tour on this bike. I wouldn't personally tour with a child trailer for a variety of reasons, but I've talked to people that have gone thousands of miles with their gear stowed in child trailers. There are other kinds of trailers that work better for touring, but child trailers can work. That's not a top of the line bicycle, and again, I wouldn't tour on it. But I've seen people do cross country rides with bikes that weren't too different from that one. You don't need a high end, or even middle end touring bike to go on extended tours. Better touring bikes do have their advantages, but they aren't essential.
Bike fit is an important issue, though. So definitely make sure that bike is the right size, and that you would be comfortable on it before you buy it.