I don't think there is a connection with my family - I'm a direct descendant of the Sidney Seager & Ann Jackson (nee Howard) you mentioned in your posted message. My Sidney whose father was Samuel was born in Hampton, Surrey and living in Kingston Upon Thames in Surrey before coming to Australia in 1854.
Do you know when your Emily came to Australia?
I had a quick look on the 1841 & 1851 English Census and found 1 Emily Sager born 1826 in the 1841 Census and none in the 1851 Census.She was born in Worcestershire, and was living in St Helens, Worcestershire.At the time she wasn't living with any family members (I think it must have been a school or some other institution as there were 8 other 15 yr old girls there at the time).There was no Samuel Sager/Seager living in Worcestershire, but quite a few living in other areas but only about 3 (Sager) old enough to be her father.There was only 2 other Sagers living in Worcestershire both name John - one born in 1816 (living in All Saints) and one born in 1821 (living in St Clements) both were labourers - so if she was at a private school I doubt that they were related.
There was also 1 Emily Seagar born 1821 born in Kent and living in Staplehurst with her parents Richard and Caroline and sister Caroline.
There were no other Emily Sager/Seagers listed in the census around the right age.
I did however find a Robert Dean (born c1814) living in Kent in the 1851 Census with his wife Emily and their three children Jane (c1844), Henry (c1848) and Sarah (c1850).They were living in Tunbridge Kent.They don't appear in the 1861 Census.If this is your family I can send you copies of the Census pages if you send me your email address.