I have 3 suggestions:
- Embroider the nose
- Make it out of a clay or from another plastic material (there are lots of options in craft stores; do some research about the most convenient one)
- Crochet the nose: I'm really bad at embroidering (and I actually hate it), so when the nose is an important feature of the amigurumi I tend to crochet it. For a hazelnut-shaped, doggy nose this pattern would do: single crochet, double crochet, single crochet in a magic ring, close MR, FO, leaving a tail for sewing. You can use either yarn of same thickness as your project (I would recommend sizing down the hook and working really tightly) or thinner yarn (even embroidery thread!).