Actually, 'dad; has been around for a lot longer than 'mum'. Both words have been used in English - in one form or another - since the 15th century. The 'mama/dada' versions are just a reduplication of a sound that babies make instinctively, as answers above indicate. In the case of 'mama', it is used in virtually all countries where the proper word for 'mother' begins with the 'm' sound, as in French, German etc.
The actual form 'dad' is far older than the form 'mum', since the former has been around for half a millennium and the latter has existed only since the early 1800s. (As 'mam', however, it's been around for as long as 'dad'.)