Simon Cowell -- 10-Day-Old Eric Flies and Soaks in Rays

Simon Cowell is not a slave to convention ... because his baby did what most don't -- and what some doctors say is dangerous for newborns ... his kid jetted to Miami for some fun in the sun.

As for flying ... there's a risk for mere mortals because of germs --- newborns are fragile because of their developing immune system ... but Simon flies private so it clearly minimizes the risk.

But some docs do advise against any flying because of pressure during the ascent and descent.