I think I've found her in the 1911 census with her Lunn grandparents at Worsborough Dale, Barnsley - RG14/27628 sch459. Age 2, born Sheffield.
They can be found in 1901 in Worsborough - RG13/4323 fo129 p12. The household includes a son Ernest (16) and a daughter Gertrude (14), so one of these might be your Gertrude's parent.
In 1911 Gertrude the elder is with Ernest and his wife Emma, and the form appears to show a 2½ year old Gertrude as well, but she has been crossed off and marked 'away' - RG14/27894 sch42.
(I also looked at the 1901 census - RG12/3782 fo35 p2; there were several Lunn families on that page, so you might want to investigate if they were related.)
Next, looking for a birth at FreeBMD, the surname Lunn didn't get anywhere, but with just the forename Gertrude there's a Gertrude Lunn Chapman in Sep qtr 1908 in Sheffield.
I suggest you look at these for yourself to check whether these all fit together. Things to consider might include:
- Gertrude's marriage certificate - what does it say about her father?
- have I found the right birth registration, which may mean buying the certificate, and if so, where does the Chapman name come from?
- what about Ernest's marriage?
(I wrote this while the others were typing so a lot of it has already been covered, but in view of the baptism Comberton has found, you'd also need to investigate the Ernest/Alfred discrepancy.)
