Eisriesenwelt is the largest ice cave in the world. It is only open in summer, but beware and dress appropriately, as it will have around 0 degrees in there, and it's very windy as well (they'll explain to you why). You cannot walk through the ice cave alone, but you'll have guide who is going to explain the geological features and stunning ice formations to you. Even nowadays, there are no electrical lights in the cave, only magnesium lamps and torches are being used, which adds to the vibe.
From the top of the cable car, it is around 20 minutes of walk to the ice cave and in the cave it's around 1400 steps. While technically also prams are allowed, I would not suggest it, as it could be tricky to keep your little one warm enough for the whole trip through the cave.
I've been here already twice, once as a school trip and once a couple of years ago with some friends, and I would do it again in a heartbeat! The melting ice and subsequently freezing water creates new formations all the time, so no visit will ever be the same.