as I live quite close to Dormagen and am familiar with refering database, I have some info for you if you are interested. But they must be verified before you add them to your tree. she might be the right Christine Burbach.
1. Christine Burbach *1863 (8 siblings born 1857-1873)
2. Her father: Johann Burbach * 19 Oct 1827 (9 siblings)
3. Her mother: Catharina Schmitz *19 Sept 1839 (10 siblings)
4. Johann Burbach's father: Christian Burbach
5. Johann Burbach's mother: Catharina Görgens
6. Catharina Schmitz' father: Hilger Schmitz
7. Catharina Schmitz' mother: Elisabeth Becker
All were born in Dormagen and baptised Roman Catholic
The Peters are from Solingen-Ohligs. The records are available in the main archive of the Rheinland in Brühl where I do research quite often.
But there was another Christine Burbach whoopn 10 Nov 1882 married a Heinrich Hausmann in Dormagen. Looking at Karl Peter's immigration record I realize he wanted to join a cousin Emil Hausmann. There might be a connection between the Burbachs and the Hausmanns from Dormagen.
All the names and data I gave you were found online. They should be looked at at the archive verify them.