I assume the entire sentence is kind of a figurative and joking expression.

>qu'elle a joli (**nez**) d'ailleurs !

The noun "nez" is most likely omitted here, so it necessitates the use of the verb "avoir".

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> les épices **lui montent** facilement **au nez**

Literally: the spices can all too easily go up to her nose.

{Or more like: = get up her nose = little things can irritate her}