Though it is difficult to tell on these small jpegs. The image of Simon is 100% vector illustration ala Gerber baby style. (On a large image, you can see pencil strokes.) Unless you will be doing all self-adhesive labels AND using offset printing, a photo halftone will be next to impossible to print using screen or pad printing.
I just uploaded a few more full color versions. The idea behind what my submissions, is to offer a look the says more baby product and read less like a postcard for a photography studio. I wanted to keep the edges soft and rounded, which is more in line to the baby market. I also want to keep the logo contained in a shape that would bring brand recognition. I'm not sure if you plan on eventually marketing this on a large scale or if will be limited to small boutique shops. Either way, getting past the store buyers, is 90% of the battle. I feel that your label will need to reach both those buyers as well as the end user. With over 27 years in the business, I can assure you that it is the store buyer that can either make or break the success of a product. Additionally, I wanted add some muted greens to the logo in keeping to the "all natural" pure theme.
I am also presenting an option of having Simon being seen as a cute cartoon figure. Please feel free to make any suggestion and/or ask any questions.