You might try
deceasedonline. Its coverage information doesn't mention Wolverhampton Council, but the burial might have been elsewhere. If the child hadn't been named, the first name will be given as "(SBC OF)" (StillBorn Child of).
You might also try Find a Grave, as the large number of memorials listed there for
Merridale Cemetery at least means it's probably one whose entire register has been uploaded. The first name may be shown as Unknown, Baby, Child, or similar if unnamed.
Entries on deceasedonline and Find a Grave can also be found on Ancestry, the former entitled "Web UK..."
It was common practice to inter a child with the next adult burial. The parents might be told it was "so that it wouldn't be all alone", but the reality was that few would want to go to the expense of digging a new grave for a child or even opening an existing one. It may well be a common grave (aka "public" or "pauper's") with several unrelated people. If you click on the name on deceasedonline's free search, it may offer a list of n other burials in the same grave, Half a dozen or more suggests either a large family plot or a common grave.
