I’ve wanted to enter doodle 4 google for the last couple of years (I’m 13 now) but I definitely don’t want to get my school involved! Can I just enter as a homeschooled kid or would they find out?

I think they would find out because I’m homeschooled online and I looked at the information and everything and the school needs to be registered and even if you were to register as homeschooled they need all the information of the homeschool system or whatever.
You can try it though.
Go to google.com/doodle4google/index.html
and go to registration, check the homeschooled box thing at the top and fill it out.