elizabeth peden, Antrim Ireland 1777-1850

The information below is what I have for Elizabeth Peden (b March 1777; d summer 1850, aged 73; Antrim, Ireland - source: Ireland census 1851, pp 430). I would like to know where I can find information on her parents, as well as other family members (i.e. siblings, etc.)

She married William Simpson, solicitor of Larne Mills, Antrim, Ireland and they had the following children:
James 1806-1848        
Dan Peden b.1807        
William 1809-1863
Agnes c1821-1902        
Elizabeth
John c1820-1859