You have the right family, but the infant on this census is reference to Amelia Gertrude born on 29 May 1880. (I have May, but census says March. I will have to further investigate this one.)
Mary is supposed to have been born and died between the 1870 and 1880 censuses. The 1880 census does not contain Mary; so I am assuming she died before this date.
I'm thinking I need access to either a Jackson County, Missouri (13 Sep 1875) birth index or certificate OR a McLean County, Illinois (17 Mar 1877) death index or certificate. I don't know if these databases exist somewhere; I haven't been able to locate them OR confirm that the databases don't exist.
Also, I don't know if there is a burial database or cemetery database for McLean County, Illinois.
Ida b. 1871 in Kansas (according to census)
Fred b. 1873 in Kansas (according to census)
Mary b. 13 Sep 1875 in Kansas (don't know where this info came from)
Mary d. 17 Mar 1877 in Towanda, McLean County, Illinois (don't know where this info came from) (don't know where she is buried)
Louis b. 25 Aug 1877 in Towanda, McLean County, Illinois (according to census)
Ameilia b. 29 May (or March) 1880 in Towanda, McLean County, Illinois (according to census)
edited to add: enumeration date on census is 22 June 1880
P.S.: I just hope that I didn't send off for Mary's info and I have simply forgotten that I did that. I don't remember. If I did, I am assuming that it wasn't a death certificate since I don't have the place of burial. I am still thinking that I don't have this information.