If the alligator becomes problematic due to someone using the exact same design, pull from other things which Louisiana is known for & which may be kid friendly.
You can also have someone make some customizations to your alligator which makes it unique. That would be fairly cheap if *not* hiring somebody like me

because I don't work cheap unless I am donating my time / skills to a non-profit.
Having other gator logos out there isn't really an issue, especially if yours is very unique to others.
And yes, think ahead, as someone else said. if you plan on using any kind of stamp - soap stamp or rubber stamp for print materials - consider your font carefully. For a soap stamp, I would likely forego the alligator as it might be too much / not work that well & use just the text. You can convert your logo to SVG format for this & other purposes, which is important unless the person who is making your stamp is willing to do this for you. There are various free online converting tools you can use for this. Search CONVERT JPG TO SVG FREE if your image is a JPG.
Another consideration is your font color choices, and whether you are saving your logo document in RGB or CMYK color profiles. Most printers I know prefer / insist on CMYK color profile. But for online graphics, you would use RGB.