The Monsters book will do. Everything you need to play non humans in RuneQuest will be there. Companion gives you just some new magic options, further background materials and some other neat stuff. Actually I'd say that the RuneQuest deluxe that is about to be published is the best way to start into the game, as I think of RQ, Companion and Monsters as the three must-have titles for the series, which will all be included in the Deluxe version.
So you might have bought the Companion in vain in regard to the non human rules, but you'll find the book handy non the less. Go get a copy of Monsters and you're really good to go!