We just did this two weeks ago. We have a stroller with bigger wheels and a little bit of suspension however. It is doable but could be a little bumpy for the baby.
It's definitely a "foot path". It wouldn't be terribly difficult to hike if you have access to a "backpack" to carry your little one in.
It would be very difficult, tree roots and down branches. I'd use a carrier if you are taking a baby.
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