I think the URL is better then the pet ID, because the URL already has the data in it if you know how to read it, that thus the generator wouldn't have to do a database look up in order to get the numbers

http://www.sylestia.com/imagebuilder.php? - URL start
species=sylvorpa
&breed=sylesti
&gender=female
&gd1=NN - Gene 1
&gd2=AA - Gene 2
&gd3=NN - Gene 3 (Note if carry, it won't show unless pet is tested)
&md1=NN - Mutation 1
&md2=AA - Mutation 2
&md3=NN - Mutation 3 (Also the letters indicate from the drop-down box, A being the top and D for example being bottom)
&ec=77175b - Eye color hex
&c1=2e2c32 - Color 1 hex
&c2=4d1d5c - Color 2 hex
&c3=f536fb - Color 3 hex
&gd1c=e67461 - Gene 1 hex
&gd2c=f7fdfa - Gene 2 hex
&gd3c=3387bb - Gene 3 hex
&md1c=543979 - Mutation 1 hex
&md2c=330542 - Mutation 2 hex
&md3c=1a053c - Mutation 3 hex
&maturity=648 - Age (648 is highest)
&size=250 - Image size