Hi Nick, not sure if you mean the back is small or the overall chair itself is small .. 'like a child's chair.'
The legs on both these chairs are original. This is normal, that the back legs of a chair will be quite plain and in fact, not matching the front legs. The back leg on the hall chair in my photo, is known as a sabre leg (curved) the normal back leg one would find in most all (four leg) hall chairs and on most dining chairs.
I don't think you are going to find a webpage or even a dealer in real life that exclusively confines themselves to hall chairs. Nor am I aware of any books exclusively on the subject.
The hall chairs, as the name would apply, resided in the hallway, (either front hall, back hall or indeed both), of the B I G house, the estate house, landlord's house and places such as your convent or other church estate houses, like the Church of Ireland rectory for example. The hall chair came in sets, the size of the set depending on the status of the house and the quality of the back (and chair itself) again depending on the status of the house and the owner. The back decoration of the chair being more or less a statement on the wealth and status of the original owner, many times incorporating a coat-of-arms, although, not always was the coat-of-arms a real one, many times merely appearing as a pseudo coat-of-arms, especially for the 'new money' owner.
Their function was simply as a waiting chair for visitors to the house, strictly no upholstery of any kind, an all solid seat and back. The lack of upholstery or textile was a matter of hygiene, as the personal cleanliness of the many visitors to the B I G house could not always be guaranteed ..... fleas/mites and other beasties don't normally live or reside on solid wood. ;>
As you are in the Dublin area (I am in the North - Co. Antrim) getting some more information and help with the chair shouldn't really be a problem. Get yourself down to Francis Street (Dublin 7) there you'll find literally dozens of good antique shops and dealers, better still (if possible) take the chair with you down to Francis Street, show it to anyone of the dealers and all the questions will be answered.
As a single hall chair, it will not *normally* have a high value. As they are a rather uncomfortable chair they serve little function today in a real domestic environment, other than for their decorative or historical appeal. It's really only sets of hall chairs that command the high prices, the bigger the set the better, set sizes can range, from a mere six up to 20+ and more ... unless .. the convent (the house) has a local history and/or the original owner was a prominent person. If the house in question has real age, then obviously it wasn't always a convent, check that out. I am assuming the hall chair belongs to the house in question, which is a reasonable and safe assumption ... the coat-of-arms on the back of the chair may (or may not) be of some assistance to the chair's original origins.