janeli, Scotland's People has both christenings listed as separate entitities so I think you have to assume there were at least two Mary Gowanlocks born around the same time, father's name Walter, both christened in Lochmaben, but no record for any baptism in St Mungo, or of any baptism in Scotland between 1799 and 1805 for a Mary Gowanlock with a father called James. Not all pre-registration baptisms are recorded so that doesn't mean that Mary, born in St Mungo to James and Phillis, doesn't exist, just that there's no record of her baptism.
I know in my own family I have my great grandmother and her first cousin born within 2 months of each other in the same place, both christened Margaret after their grandmother, but then their fathers were brothers and had different names so we eventually disentangled them. For you it's more complicated as two of the 3 possible fathers are Walter Gowanlock, possibly cousins, who knows?, so there'll be more detective work needed to divide them up.
The basic SP search brings you:
5 December 1800. Mary Gowanlock, daughter of Walter Gowanlock and Margaret Jardine at Lochmaben. GRO reference to view the whole thing 840/00 0010 0116
26 April 1801. Mary Gowanlock, daughter of Walter Gowanlock and Tinnie Bettie, also in Lochmaben. Reference for that is 840/00 0010 0118
These confirm the details you've found on the Canadian tree, and on IGI, but if you are absolutely sure that your Mary was born in St Mungo to a James and Phillis, then it doesn't look as if either of them relate to her.
This was still bugging me, I felt I'd missed something then realised I had searched the name as 'Exact' instead of 'Traditional soundex' Going back and searching 1799-1806 again I found these 3 baptisms, all in St Mungos:
19 Sept 1799. Janet, daughter of James Gowenlock GROS ref 847/00 0010 0131
15 Nov 1801. Mary, daughter of James Gownlock. GROS ref 847/00 0010 133
28 May 1804. Philis, daughter of James Gownlock. GROS ref 847/00 0010 0135
There may have been more baptisms in the family pre-1799 or after 1806. I suggest you go into Scotlands People and have a look for yourself, it's not an expensive subscription site - you only buy credits for searches and for whatever original records you choose to view.
You say you had a birth date for 'your' Mary of 15 November 1800. That is not likely to be a birth date, whether your Mary or not, as that is given as the date of her baptism. It is quite rare to get birth dates recorded, but the date of baptism, taken with ages declared in later records, usually gives you a clue. (unless like some of mine they did baptism job lots for several children aged babyhood to 10 altogether, in which case it doesn't help at all) Still with 3 baptism spread across those few years it would seem to indicate that James had his daughters baptised when babies.