Pineywoman, offhand I can't think of any section of the Batona Trail that doesn't have some areas of soft sand. But more of a concern than soft sand is chiggers, which are at their worst in September on the Batona Trail. Brush up against the wrong weed, bush or grass, and you and your infant child are going to be covered in bites. A frost or a few nights in the 30's should kill them off in about a month. If you're going to risk it, I would pick a cool morning. Chiggers are inactive in temperatures below 60 degrees.
At the Brendan Byrne State Forest, there is a cranberry trail (red blazed) that stars about a hundred yards right of the entrance door into the park office. It is a bike path trail that goes to Pakim Pond (3 miles one way) It would be fine for strollers. You have the option of taking the Batona Trail back to the Brendan Byrne office parking lot, or a paved road. But again, I would caution you of the risk of chiggers if you brush up against some of the weeds that dot the bike path.