I'm looking for a word that describes this happy fellow:
I don't think frothing is the right word. It isn't froth or foam, but sticky wads of spit.
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The word slobbering comes to mind.
More often used to describe the drooling of a dog but is perfectly acceptable for the picture given.
Spittling works as a rare present participle of spittle, most often used to refer to spit when ejecting from the mouth.
Sources: Googling "define spittle" gives the definition, "saliva, especially as ejected from the mouth." I believe Google get their definitions from the Oxford English Dictionary.
We often use the verb:
... to indicate someone spitting whilst speaking loudly, aggressively or when very emotional. Here's the link to the word in the Google dictionary: spluttering
Try GLEEK. It refers to the squirt of saliva ejected involuntarily when you open your mouth. Most common when you are salivating over food expected to be special but I think in this instance it fits.
https://www.google.com/search?q=gleek Link brings up several pages of information.