I'm thinking uneasy truce is likely to be the best you can hope for under the circumstances --- phobias, as I'm sure you realize yourself, are not easy to cure in 'rational' ways; irrational fear that is *not* an outright phobia is. Hard to distinguish sometimes, though, even for medical professionals --- and especially at this young age.
And this is my cue to confess, with great embarrassment, that I've not taken a shower in two days because... there is an eency-weency little spider sitting in a corner of the tub. It's spindly grey and a little bigger than my thumbnail. Now, I'm scared of spiders. I no longer scream in terror or leave the room altogether (that would be very problematic, this being the bathroom), but I *cannot* muster up the courage to shoo poor spidey out of the tub, lest she decide to run up my arm or something.
You can now christen me Miss Muffet, but what I'm trying to point out is that I live in a house quite lively with spiders, geckoes and other insects --- and proximity has not entirely cured me. At best, I can do the dishes *knowing* there is a spider or three under the sink --- but I remain antsy and ready to bolt at a moment's notice. Cockroaches and geckoes get the same reaction from my SO, but don't bother me in the slightest! So Jack Sprat etc.)
So again, with your niece, you're likely best off ensuring distance and calm between canine and child --- until she has enough of a grip to at least not scream or shiver uncontrollably.
As for *why* she's scared, that's maybe something to try asking her. Though of course if it's a far enough memory, she won't really know. I used to howl at the sight of my grandmother as an infant (of all things! much to my other grandma's great distress!); and then froze and screeched at the sight of two of my uncle's friends (no connection between them, nice people both, and I have no idea why --- though I suspect it *could* be that they looked like a couple of other people each, and I had once been unintentionally 'tricked' into going away for a walk by the river with my favourite uncle's identical twin, realizing I had the wrong bloke carrying me only when I saw the right twin!)
Fears often are irrational and unfathomable, even when not uncontrollable phobias. Mine, of spiders, began as just a general fear of creepy-crawlies and turned into full-blown panic only after my Dad got bitten by a venomous one in Australia (we never saw it, and it only gave him a sore and swollen toe for a long time). Interestingly, I have no issues with the radioactive spider biting Spiderman --- so I guess my brain is rational enough to recognize 'not a threat to self, so don't panic yet'!
Good luck to you, to Kona and the kid arriving at an understanding!