From what i have read, the 1st generation nano has never had a software update. Bear in mind that the nano (and the Classic) have never needed as many updates as the Touch, so it's possible that your iPod already has the up-to-date version.
The best way to find out is to connect the iPod to iTunes and get iTunes to check for you. If there is an update, iTunes may even tell you before you ask. If there is no update, iTunes will not tell you anything, in which case you ask it to check for you, just to make sure.
Look at this as a challenge and adventure for your child. If the iPod is seen by iTunes and you manage to put music on it that he/she likes, let's suppose that he/she finds it all very boring. You've lost nothing, but you will have gained a bit of parent-child bonding time. On the other hand, if your child is so taken by having his/her own choice of music available whenever required, you will have not only gained that parent-child bonding time, but you may have found his or her life-long passion.
That's what happened to me. At ten years of age I realised that I could buy make my own choices and recorded music (on vinyl, CD and now MP3) has been my life-long passion. That discovery was 53 years ago!
Connect it to iTunes and see what happens. Let us know, either way.