Hello,
Search done on the IGI - no luck for her birth or of children born to John Bailey and Grace. As Falkryn states and Scotlands People website clearly points out - up to 30% of births are not on their site for various reasons. One of those 'stops' in family history.
The IGI has and 'extracted' record of Grace Bailie marrying Abraham Walker on 04 Jan 1846 in Lanark
Children from this marriage according to the IGI:
Grizzel Walker ch. 02 Jul 1848, Lanark
William Walker ch. 10 Dec 1848, lanark
Grace Walker 12 Oct 1851 Lanark
(There is only one Grizel Baillie recorded on the IGI in that timeframe but she's not yours - f. George Baillie and m. Mary Pringle. She was born 04 Apr 1822 in Jerviswood, Lanark - 'submitted' record).
On the IGI from 1805 to 1825 only one record of a 'Grace Mathweson' marrying - and she's not yours. (The good thing about the IGI is that it automatically searches for variants of names).
Good luck with your searching - Regards, Steve