Whether the falls are flowing well or not, this is a neat hike in the Sequoias Wander through shady groves and around giant fallen trees. Try starting on this trail early to avoid the crowds -which aren't that bad anyway. It's a peaceful stroll in contrast to the amusement park vibe down at the General Sherman tree.
The hike is mostly flat with some rolling inclines and steps to the top of natural granite viewpoints. Making your way further toward the trail's terminus, you'll find more granite rock than trees. The last eighth-mile or so will have you doing some light scrambling, squeezing through and ducking under large boulders. It's like nature's own funhouse. Total elevation gain is an easy 600 feet and should be no problem even with a loaded child carrier. A mile nonstop is a bit much for little legs, take breaks in the shade often.
The end of this out-and-back trail is Tokopah Falls, a thousand-foot cascading waterfall. My recommendation is to have lunch or a big snack at the end of the trail. There is space for kids to rest or climb around on rocks here. Be careful, rocks on the cliff-edge of the trail are dangerous and probably slick when wet.
You're probably going to see a bear or two. And if you don't see them, they probably see you. Bring bear spray and read up a bit on how to use it, if that makes you feel safer. Bears on this trail seem to be very comfortable with humans around. That's not to say they are approachable AT ALL, but it's best not to panic and mind your own business as they forage about their home.