Civil registration commenced in Tas in December 1838. Before that date the records that you see in the indexes are church baptisms, marriages and burials. Even after civil registration, many (some of us would say most!!) events were still not registered. If a child wasn't baptised (or the church records have not survived) and also wasn't registered then there will be no record. Depending on the status of the parents you may find a birth announcement in the newspapers instead.
If you can't find a registration after 1838 then the church records at Tas Archives are definitely worth searching as this has solved many people's family mysteries.