Just a couple of thoughts (from a mom):
I find that fish in quarantine/hospital tanks require a lot of observation - and I do a lot of my observing after my children have gone to bed - so I would personally hesitate to keep in the child's room. Also, many sick fish don't survive - and if my 5 year old was more attached because it was in his room, this would potentially create a lot of unnecessary tears. But your child/situation may be different.
Also - I have found that when I have fish in quarantine or hospital, it is RARELY for just a few days - often requires 1-4 weeks of attention. IME.