Here is one of my proposals. Instead of creating a separate icon / typography combination, I've created an all encompassing logo / unit. One that can be used for additional elements just as branding stamps, watermarks, shirt badges/embroidery etc.
There is also a subtle hint to "natural" - in the base of the "y" in baby, in the negative space I've created a leaf.
The logo is 100% vector so will scale well to any size, and works well in full colour, B&W and on coloured backgrounds if needed,
It would be my pleasure to work up any variations so please do say. I look forward to your comments or thoughts.