Hi Mark, what a great project and it sounds like you are having fun already?
I just read your opening post and wonder about your logic regarding your one year old verses a J tube!
Firstly I will just say that I really like J tube’s designs, they make a lot of sense for many applications, relatively simple to build and very easy to use.
However the open top fire box will be an irresistible draw any child of any age and a perfect hight too!
Something like shorty batch box design can be set quite high off the ground and also have a door.
Secondly I would advise reading up on the use of any high temperature matting or wool, its use is very popular on this forum but as an example, if you use it inside your bell and you get a down draft of wind (very common with open top J tubes) you could be allowing your room to be contaminated with potentially toxic dust.
Of course that is totally up to your discretion as the product is very effective but does come with some risk!
Your ideas about building an internal brick chimney is unusual but sound….. and should be very long lasting, the down sides might be the work and cost involved or maybe the fact that you just can’t check to see if it has cracks or leaks but that would also apply to any internal chimney. Something like a cast iron pipe or stainless steel pipe might be an option.
You may want to look at cement board and find out what is available near to you. I often use high temp cement board for chimney construction. That would be long lasting and simple to use.
Vermiculite board would kill two birds with one stone as it is very insulating and also very easy to work with.
Good luck in any case……