I do not find “dragonslay”, “dragon-slay”, “dragonslayer”, “dragon-slayer”, “dragonslayings,” or “dragon-slayings” anywhere in the most common 100,000 words of the Project Gutenberg corpus!  I will double check, as this is a quite unexpected finding.  Neither is it as a single word (even a two-word single entry) in the OED.

• 12.090 and they all began discussing dragon-slayings historical,
• 15.056 as the dragon-slayer,

Much turns on this concept in the novel… but it is named only once, an original JRRT word.

• 19.044 he fell under the dragon-sickness,

This word is not attested in OED.

• 14.027 Bard the Dragon-shooter of the line of Girion!

There are night-noises in the OED, but no dragon-noises.

• 13.029 and still there were no dragon-noises,

This word is nowhere in OED.

• 10.007 under the shadow of the distant dragon-mountain.

In this case it is lore about dragons, not lore known to dragons.  This word is not attested in any form as a single word in OED.

• 12.046 in dragon-lore as all that,

Although every dragon needs a proper hoard, considering it one word is not attested . in OED.

• 12.015 and sing of dragon-hoards before,

This beautiful image word is nowhere in the OED.

• 13.051 of the dragon-haunted caverns,

It is not attested in OED with a hyphen, a space, or as a single word.

• 07.013 They offered him dragon-gold
• 07.013 and I think I have earned already some of your dragon-gold –

This beautiful word is not found in OED hyphenated or compound – it is JRRT original for our purposes, and much used by modern fantasy authors.  And my favorite form of the word?  Right here.  The ultimate lullabye.

• 01.076 The dragon-fire, in twisted wire
• 13.009 But certainly it was not a spark of dragon-fire,
• 14.033 Dragon-fire and ruin!
• 15.039 The dragon-fire, from twisted wire