I wouldn't worry too much - as you mention - she's a new dog, and a rescue. It takes time from a dog from a rescue to 'settle down' and learn to trust a new owner. This process can quite easily take months.
So don't worry too much.
Now - we had a similar problem with ours - a dog from a rescue, about a year old - who decided that she really disliked the car harness. Not to the same degree, but definitely and distinctly 'didn't like it' - and would run away and hide whenever we went near it.
We still don't know entirely why - but it has settled down given time.
However I'd suggest there's two likely root causes - either it's because it's uncomfortable, or your dog as formed a negative association as to the wearing of it.
For the former you can address this by checking the tightness, and inspecting the neck area. Also consider how the collar does up. We stopped using the buckle style collar, and instead went for one like this: http://www.ezydog.co.uk/neo-collar-wide/
It's a wider band (so less likely to 'cut') and with a clip to do it up. It's adjustable, so you can set it to exactly the right side for the neck (although, her neck does seem to widen and shrink at times!).
A combination of this with using high value treats to bribe (pieces of liver, tripe sticks work very well) helped keep her distracted long enough.
We also bought another harness that didn't go over the head - http://www.ezydog.co.uk/chest-plate-harness/ - but didn't get as far as using it.
If it's anxiety brought on by an association, then the trick there will be desensitisation. Work 'collar drill' into training regime - put it on, take if off again.
Put it on, do something fun, take it off again. Add treats. Make 'putting collar on' mean 'good things happen'. Usually it being walkies is enough, but you're going to need a bit more.
Don't worry too much though - your dog is still settling in, and chances are it's still learning boundaries.