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Im trying to export a 3d model from qgis2threejs plugin in Qgis, but all I've managed is to export my DEM, without any data. Is it possible to export a 3d model in some of its extensions (STL, COLLADA, Wavefront) to look like a model in qgis2threejs pluging, with data and colored DEM?

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Sadly "no" is the short answer. The longer answer is "not in the version 2.x for QGIS 3.x". The change-log states the following:

Disabled/removed these features: DEM advanced resampling mode, 3 object types (Icon, JSON/COLLADA Model), some object specific settings for Profile and Overlay, FileExporter (Save as STL, OBJ, COLLADA), GSIElevProvider.

However, you can export to glTF, a format for 3D printing. I don't know if the other formats are earmarked to be brought back (that would be awesome if they were) - so maybe keep a watch on the web site.

If you need to export in one of those formats, you could install an older version of QGIS with the QGIS2threejs v1.4 plugin or you could use one of the other routes to 3D involving 3D modelling packages (search this forum - there are loads of threads about it). Another interesting development to watch is QGIS-X3D-processing.

One more option to consider is the GRASS nViz tool (available via the processing tool box). nViz can export to a variaty of 3D formats including VRML, POV-Ray, kml and dxf. This would not be my preferred option (definitely not VRML - I used to go that route years ago but VRML is ancient tech now).

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At the moment (01.2021), there is an editor directly on the three.js website which enables a direct export in many formats.

From my side the models appear black on this web-editor but the colors are maintained as soon as exported in .dae.

This scientific paper is also worth reading.

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