As mentioned in the comments the cartoon-style black outline is an image only effect done internally in post production over the rendered image, it does not affect the model nor is it part of the geometry, there fore it cannot be exported in any file format other than an image render, or at best as an SVG vector file (using the *Freestyle SVG Exporter* addon) you can then place over your image.

Where are you exporting your model in COLLADA too? Some Game engine? Other modelling application? You most likely need to recreate the outline effect there in the destination.

Otherwise if you actually want to have it in-mode there are a few options.

 - Either us a wireframe modifier over your objects to construct a cage-like structure over you mesh
 - Use a Bevel modifier on your mesh with a material index offset
[![enter image description here][1]][1]
 - Manually bevel your texture
 - UV Unwrap your model and use an image texture, created in an external image editing software with the desired edges in place.


  [1]: https://i.sstatic.net/8eqEt.jpg