I'm pretty sure they don't let dogs on golf courses. Something about "digging holes" or something similar. Of course, there aren't many four-year-old kids on them, either.
This is the second reference to baseball in the strip, and the first that shows the kids actually playing. It looks like Patty can really belt the ball, just like her later namesake Peppermint Patty.
It won't be much longer before Snoopy starts using thought balloons, and this joke wouldn't work if they were in use. Did Schulz plan it that way, getting the joke used while the using was good?