Almost certainly you'll cause agglomeration and aggregation of your particles if you dilute in DI water. Ideally you dilute in the mother liquor - the same ionic make up as contained in the continuous phase in your stock solution.
As Ms. Bora said it is best to determine size by using DLS and it will give you hydrodynamic diameter. You can also find nanoparticle size from TEM image and some image processing software.
However, if you just want to ensure size distribution but not size, DLS should be fine.
I am re-reading the question and it appears from your statement "Actually I have 1 g AgNPs, now I want to mix with water. How can I assure its dissolution/dispersion in water uniformly?" that you have a solid material. Am I correct? If so you can never re-disperse the solid to nano-form where you have free discrete particles in colloidal suspension. See:
Nov 11th, 2008. Dispersion and nanotechnology http://tinyurl.com/hpywsge