The Snowflake Chunky is a thick fuzzy textured yarn, no doubt this is what makes the "furriness" of the poodle. You could substitute Bernat Soft Boucle, Caron Bliss, or JoAnn Casual Boucle.
The DK is a smooth thinner yarn. You could use Bernat Sweet Baby, JoAnn Cuddle, or Lion Brand Babysoft.
The difference in needle and hook sizes from different countries can be confusing, can't it? I remember going into a yarn store looking for a 4.25mm size 6 needle, and being told there is no such thing. In the USA the size 6 is 4mm.
The nice thing about making a toy such as your poodle is that gauge is not as crucial. So what if yours is an inch or so larger or smaller than the pattern? Go with the needles closest to the size called for and you should be fine.