Child support is paid to take care of the child. Sure. Charge for the care of the child before it's born. Big woop.
You can't deport a woman that's carrying a US citizen after 6 weeks of pregnancy? Sure. Why not as long as the child can't automatically be a citizen just because it's born in the U.S. The child has to be in the U.S. before the mom hits her 6th week of pregnancy. I'll take that one any day. We should start by deporting the chick and her kid when the chick climbed over the border fence at 9 months of pregnancy. Yay.
Insurance? Insurance is a private business. If you can find one that will insure a 6 week old fetus, go for it. Btw, as far as I know, NO INSURANCE COMPANY will sell life insurance for any child less than 14 days old. Good luck.