Axel Anders Petersen was born 10 January 1887, baptized 06 February 1887 in Svendborg at Sct Nicolai church. The Danish Archives Online (AO) reference is 1876-1887 opslag 46.
I didn't find the family immediately at ddd.dda.dk, an easy site, so I googled the names as the next easiest method, and found a post by a Pauline on an Ancestry.com message board, dated May 2012. All this information was given by a kind soul in reply to that post. This is most certainly your family. ; D
In 1890 the family lived at Svendborg Købstads Bymark in Svendborg Købstad, in Sunds herred, in Svendborg amt, in Denmark. The father is not mentioned in this census.
1890 Dansk Folktaellinger, Svendborg, Sunds, Svendborg Købstad, Svendborg købstads Bymark, , Øksenbjergmark nr. 684, hus 1 fam, FT-1890 * Vilhelmine Pedersen age 25 married husmoder (mother of the house) born in Bregninge, Svendborg Amt * Axel Pedersen age 3 unmarried, son, born in Svendborg * Jens Pedersen age 1 unmarried, son, born in Svendborg
In 1901 census the father is shown with the family. I've put question marks where the census is hard (for me) to read. * Laurits Petersen born 10 September 1853? in Ærøskjøbing, Svendborg? (the poster said he was a blacksmith but that is not what the census says - I can't read it) * Vilhelmine Andersen born 06 March 1864? in Bregninge, Svendborg * Axel Anders Petersen born 10 Jan 1887 in Svendborg * Jens Otto Petersen born 7 Aug 1888 in Svendborg * Laura Helene Jakobine Petersen born 29 October(?)1890 in Ærøskjøbing? * Karl Vilhelm Petersen born 13 May (?) 1894 in Ærøskjøbing? * Dagmar Hansigne Petersen born 30 June (?) 1896 in Svendborg * Vilhelmine Marie Petersen born 07 Sep (?) 1898 in Svendborg