I am connected to Peter Walker from Tippithill farm and I obtain much of the information from the McClure tree on Ancestry and they had Agnes Andrew born abt 1799.
Ah. You originally said 1790 - I assume 1799 is a typo as Agnes' eldest child was born in 1812.
I know that the LDS have a practice of assuming, in the absence of other information, (a) that a couple's marriage was a year before the birth of their first child and (b) that women were aged 21 when they married. This isn't entirely unreasonable, though in my experience most women, or at least those in my tree, were a few years older than 21 when they married. Applying this logic to Peter Walker and Agnes Andrew would result in a guess that Agnes was born about 1790.
If the compiler of the McClure tree either copied from the LDS at FamilySearch, or worked it out the same way, then what you have is a guess, not a genuine or reliable date of birth.
If you take a look at Amy Cunnigham's post above she said she had a handwritten note that Agnes Andrew was the daughter of Elizabeth Patton who had an illegitimate child Elizabeth Burns to the poet Robert Burns.
Yes. I saw that, and also noted that Elizabeth Paton or Burns was born in 1785 and therefore cannot be the mother of Agnes Andrew born c 1790, or indeed anyone old enough to be married and having children in 1812 when Agnes' first recorded child was born.
On Robert Burn's biography it said that Elizabeth Paton married John Andrew 1788.
It is absolutely correct that John Andrew and Elizabeth Paton were married on 9 February 1788, in Tarbolton in Ayrshire. At the time Robert Burns' illegitimate daughter Elizabeth was aged only two; she was born on 22 May 1785 so had not had her 3rd birthday by 9 February 1788.
Given the Walker family tradition of descent from Burns, and the impossibility of them being descended from his daughter Elizabeth Paton or Burns, I wondered whether the Elizabeth Paton who married John Andrew in 1788 was the
mother of Burns' daughter? Then Agnes Andrew would have been the half-sister, not the daughter, of Elizabeth Paton or Burns. This would be consistent with the statement in Burns' biography that Elizabeth Paton married John Andrew, and with a slightly garbled family tradition of a relationship to Burns being handed down in the Walker family.
So I had a look around and indeed the Wikipedia article on Elizabeth Paton describes her as 'later Elizabeth Andrew of Lairgieside, daughter of James Paton. It also says that she had four children to John Andrew. The relevant part of the Burness web site
http://www.burness.ca/p94.htm#i940 also says that Elizabeth Paton, mother of Burns' daughter, married John Andrew.
So I think that is the answer to the Burns connection and to the parentage of Agnes Andrew.