Here is a good link it is the state code for tenants rights with regard to your landlord and lease.
http://www.oag.state.ny.us/bureaus/real_estate_finance/pdfs/tenants_rights_guide.pdf (broken link)
I would proceed with this in a CYA fashion. As you explain it, the lady does sound like a problem and probably use to getting her way or just being in charge.
If you have not met with the lady you might want to try that and state you are familiar with tenants right and tenant to tenant consideration. See if you can just defuse her and move on.
If that does not work and she continues to contact the landlord, then you need to also in a certified letter.
I would write a short letter similar to what you posted, that you are in the middle of moving in, your dog is not disruptive and none of the other tenants have complained. Explain you are familiar with NYS tenant rights and proper neighborly interaction.
Although this is not a tenant-landlord issue you want to make sure it does not become one.
On page 28 under the heading Harassment your rights are outlined if the LL was harassing you but in this case the lady is harassing you by complaining. He may have a level of responsibility to defend or ensure your quite enjoyment.
This is all somewhat reversed, your being accused of being noisy and disrupting the piece and her "quite enjoyment" rights.
Here is a link on quite enjoyment
Quiet Enjoyment
This is a link on noisy neighbors
Noise -- How to Get Neighbors to Turn Down the Noise
You have started in the right direction, try to understand and learn your rights.
I am a LL here in NJ although the statute is different NJ has more to read which may shed some more light
LSNJLAW - Tenants' Rights in New Jersey Chapter Index
Then there are tenants organizations designed to buck the LL but may also help in tenant vs tenant issues.
Tenants & Neighbors Home
As you stated she seems like a BOW and maybe she is or it was just a 1 time thing and you will not hear from her again.
But if she is a BOW you just need to know legal rights you have to flatten her wheels.
If your accurate on your noise level and your dogs then you should have no problem.
There are also city ordinances with regard to noise and noisy neighbors which outline specified times of day that a tenant can have loud music, parties, etc and although she sleeps during the day it is not you responsibility to accommodate her schedule.