1784 or 1782 Margaret Pearson birth 

see also Jane Pearson &  John LANKSHEAR

Anthony had her as Jane Margaret and I did search for that at first - then 1841 and 1851 she was Margaret. First I thought that was a second wife per 1830 marriage of a John to Margaret Smith but now clear that was the couple who went to Tasmania. So my Margaret is the one in the census and indeed is from Scotland. I am now 3/32 Scottish - no wonder I like the Pipes. 

see 1841 Census John Lankshear and Margaret with Jane Mary - Margaret reported age as 58 so born 1782 -1783

1841 June 6th  age 58 so born June 1782 to 6 June 1783
1851 March 30th age 69 so born March 1781 to 30 March 1782

So likely born first half 1782

2001 or so when I thought she was Jane Margaret I asked on GenForum message board and SKS supplied as follows 
have Jane Pearson christened (not born) March 1784 St.Mary St. Marylebone road St. Marylebone London father Anthony Pearson mother Jane
(not ours) I have John Lancashire christened July 1785 same church as above father Richard mother Sarah

Looking at IGI for Baptisms in Scotland c1782 - nothing conclusive

MARGARET PEARSON see IGI MARGARET PEARSON
Event(s): Birth: Christening: 07 APR 1782 Auchinleck, Ayr, Scotland
Father: HUGH PEARSON  Mother: JEAN MCMILLAN
siblings presumably - but no names given to her children - mother is Jean ie Jane as per her daughter
CHRISTIAN PEARSON Christening: 13 MAR 1785 Auchinleck Father: HUGH PEARSON Mother: MAY MCMILLAN
MARION PEARSON Christening: 30 JUN 1776 Auchinleck Father: HUGH PEARSON Mother: MCMILLAN
CHRISTINE PEARSON Christening: 21 JUN 1778 Auchinleck Father: HUGH PEARSON Mother: MCMILLAN

MARGARET PEARSON
Event(s): Birth: Christening: 04 AUG 1782 Dunbar, East Lothian, Scotland
Father: THOMAS PEARSON Family Mother: MARY ROBISON
siblings presumably - well a Janet could be used for her daughter Jane - father is Thomas as per 2nd child
CHRISTIAN PEARSON Christening: 03 MAY 1790 Dunbar Father: THOMAS PEARSON Mother: MARY ROBERTSON
JANET PEARSON Christening: 20 JUL 1794 Dunbar Father: THOMAS PEARSON Mother: MARY ROBERTSON

MARGARET PEARSON note Birth not Christening

 (brother is a John and Margaret's 3rd child was a John - but neither parent's names were used)
Event(s): Birth: 07 SEP 1782 Edinburgh Parish, Edinburgh, Midlothian, Scotland
Parents: Father: JAMES PEARSON Family Mother: ELIZABETH MOFFAT
sibling presumably mother is a MOFFAT but different first name
JOHN PEARSON Birth: 24 APR 1784 Edinburgh Parish Father: JAMES PEARSON Mother: MARTHA MOFFAT

MARGARET PEIRSON (mother is a Margaret but father and siblings no relationship to names used for her children)
Event(s): Birth: 24 AUG 1781 Christening: 26 AUG 1781 Dunfermline, Fife, Scotland
Father: ROBERT PEIRSON Mother: MARGARET BIGBIE
siblings presumably
JAMES PEIRSON Birth: 03 DEC 1777 Christening: 03 DEC 1777 Dunfermline Father: ROBERT PEIRSON  Mother: MARGARET BEGBIE
ANN PEIRSON Birth: 29 APR 1779 Christening: 09 MAY 1779 Dunfermline Father: ROBERT PEIRSON Mother: MARGARET BIGBY

MARGARET PEIRSON (too late)
Event(s): Birth: 04 SEP 1783 Christening: 05 SEP 1783 Kilmany, Fife, Scotland
Father: ALEXANDER PEIRSON Family Mother: MARGARET DUCAT