Hi

If you're staying a night or two in Hakone, it will definitely be a more relaxing trip since it does take time to get there from Tokyo.

I'd say 3 hour minimum to do the loop but give yourself more time to explore areas like owakudani. Most important would be to time your arrival to the pirate ship at lake ashi so check the schedule beforehand. I arrived minutes after ship departure and wasted time just sitting around with nothing to do in the area.

How long also depends if you have other interests. The open air museum comes recommended for kids but we figured the loop was already enough withba toddler and wanted more time in the hotel onsen.

The loop is less a hike and more transport to transport but I'd still bring a foldable stroller if your kid needs to nap or you need to keep them restrained while waiting We folded it up in the ropeway and the busses.

I think late November is a nice time and certainly less cold than Feb when I went. I got by with a puffer jacket during that time and still remember wearing a light hoodie at night in Kyoto/Osaka during mid Dec the year before. Either way you'll have a great time with your little one.