If babies were isolated, would they develop their own language? Let’s say that two or more babies/infants from the age of 0 were put in an environment without the affection of adults to teach them how to speak. Would the babies after 13 or so years develop their own language? 

Let's assume that someone or something would take care of the babies, giving them food and water and so on, but never speak to them.
This question would require an experiment that cannot ethically be conducted, but it is interesting.

Wikipedia has an article on historical attempts at language deprivation experiments:


  An experiment allegedly carried out by Holy Roman Emperor Frederick II
  in the 13th century saw young infants raised without human interaction
  in an attempt to determine if there was a natural language ...
  "foster-mothers and nurses to suckle and bathe and wash the children,
  but in no ways to prattle or speak with them ... But he laboured in
  vain, for the children could not live without clappings of the hands,
  and gestures, and gladness of countenance, and blandishments." ... 
  James IV of Scotland was said to have sent two children to be raised
  by a mute woman isolated on the island of Inchkeith, to determine if
  language was learned or innate. The children were reported to have
  spoken good Hebrew ...


While these experiments had the advantage of a lax ethical environment, they also had a major disadvantage of poor methodology, and the accuracy of their documentation is very questionable.

There are quite a few documented cases of feral children, but none that I'm aware of who were raised together so as to have had an opportunity to develop language.

The most compelling case for the innateness of language development that I'm aware of is the Nicaraguan sign language (ISN):


  ... a sign language that was largely spontaneously developed by deaf
  children in a number of schools in western Nicaragua in the 1970s and
  1980s. It is of particular interest to the linguists who study it,
  because it offers a unique opportunity to study what they believe to
  be the birth of a new language.


These children were in fact raised as normal children, but were language isolated, with no contact with other deaf children until school age.  Some variables not well controlled for here include that they were exposed to the concept of language, were aware that other people communicated with each other, and already had a proto-language (mimicas).  Nonetheless, they appeared to develop a proper structured language fairly quickly upon being introduced to each other, without any apparent support or encouragement from adults, who were entirely unfamiliar with any sign language.

There are similar examples of isolated sign-language development, such as ABSL and MVSL, but the problem with all of them is that the actual level of language isolation is not well controlled for, and hence not clear.