The only birth registration I can find for Clara Pugh, born Ludlow, is in Sep qr 1854, 6a - 461.
These are the details given in the 1871 and 1881:
1871 - RG10/2692, folio 68, p 6.
Tupsley, Herefordshire.
Clara Pugh, 16, General Servant, b. Ludlow.
1881 - RG11/2583, folio 56, p 7.
Munsley, Herefordshire.
Clara Pugh, 24, General Servant, b. Ludlow.
So - I think she's too old for the Clara living with her grandparents in 1861 - and this is her in 1861:
1861 - RG9/1835, folio 110, p 11.
St Lawrence, Shropshire (which is Ludlow)
Mary Pugh, Head, S, 31, Dressmaker, b. Brimfield, Herefordshire.

Pugh, Daughter, 9, Scholar, b. Ludlow.
Clara Pugh, Daughter, 7, Scholar, b. Ludlow.
So is this Clara a red herring - as she is too old for your Clara - or was the age on the marriage certificate wrong as well as the father's occupation?
I think that it would be worth trying to find Rambler's 1861 Clara in other censuses. She is a better match for age.
Monica