Hi, She is in the 1911 census on this page http://interactive.ancestry.co.uk/2352/RG14_31314_0521_03/39314573?backurl=http%3a%2f%2fsearch.ancestry.co.uk%2fcgi-bin%2fsse.dll%3frank%3d1%26gsln%3dallan%26rg_81004011__date%3d1908%26rs_81004011__date%3d2%26f17%3dCarlisle%26prox%3d1%26db%3d1911england%26ti%3d5538%26ti.si%3d0%26gss%3drfs%26so%3d3&ssrc=&backlabel=ReturnSearchResults
it lists her as a Nurse age 2 (great, transcription Ancestry!) what it should say is Nurse child, in which case it's hard to tell the parents from that.
So you may need to send for the birth certificate which you will find under the spelling Allan not Allen here is a link to that http://www.freebmd.org.uk/cgi/search.pl
604 Sep 1908
You can send for the certificate from http://www.gro.gov.uk/gro/content/certificates/default.asp
Hope this helps