Skillset as a single word is in Wiktionary. I didn't see it in any other dictionary. A few of them have the two-word form. However the single-word form seems to have been growing in use quite rapidly over the past dozen years, according to the News on the Web corpus.
Here's a very recent example, from the UK paper the
Evening Standard, in an article published yesterday about smart fridges:
And the smart abilities have evolved too, mostly shifting away from the ‘for the sake of it’ internet-fridge trickery of the opening volley of the 21st century and settling instead into a more refined skillset of ‘things that people actually need’.
So it seems it's not just people who have skillsets these days - domestic appliances have them too.
I'll add
skillset as a rare word.