Hi! I think you will be able to find some good active activities along the way. With one exception, I don’t think you should consider ice caves in September. It’s too warm, and if the caves even exist they would be unsafe.
Here are a few ideas off the top of my head:
– Lots of the south coast won’t be a problem. Seljalandsfoss waterfall, Skogafoss waterfall (both right off of Ring Road), Reynisfjara and Dyrhólaey. In our brief daily update about Dyrhólaey, you can see my wife wearing a baby carrier in one of the pictures.
(Read up on the “sneaker waves” at Reynisfjara!)
– You couldn’t do an organized glacier walk with a child in a carrier, but you could walk up to the base of Sólheimajökull Glacier. Here’s what I wrote toward the end of that post:
“If you have kids under 10, or the glacier walk just isn’t right for you, you can also park out here and walk by yourself to the glacier’s edge. You should NOT walk on the ice without a guide, but you can hike to see it, and then buy some hot chocolate when you return.”
– Into the Glacier is the only tour I know of where you can take kids of any age. It’s out of the way and expensive, though you may enjoy it!
– You can take kids on many whale watching trips. We like and recommend North Sailing in Húsavík, though Húsavík is about half an our off of Ring Road. On their web site, North says: “Children of all ages are welcome and it’s also fine to take strollers with you on board. We recommend to dress the children warmly and ask about weather and sea conditions before you decide to go.”
– Most hikes should be fine with a child in a carrier. There are dozens of options, and you can stop anywhere that looks interesting. For some reason, I am thinking of the hike up Hengifoss in East Iceland as one that was challenging but rewarding. My 7-year-old handled it with me, though he was tired by the end!
Hope that gives you some ideas.