No genetic testing ( Down syndrome)

My doctor  hasn't done any blood work except for sugar ,basic and hiv. I'm 20+2 weeks . My last two pregnancies  I had them done early but this doctor is so OLD school . He's been my OB for three year I might add.  Shouldn't I have had something by now? 
COMMENTS would be VERY much appreciated.
Happy holidays🎅🏼🎅🏼 to all you mommies