There are potentially some siblings showing for Joseph showing as born/christened in Edinburgh. These entries show on the Old Parish Registers for Edinburgh on
www.scotlandspeople.gov.uk:
15/09/1825 Elizabeth Stewart
27/03/1831 Joseph Stewart
31/10/1834 Emley Stewart
There looks to be a number of couples with the same names, a number of births/christening show in various places in Perthshire for a couple with these names so you need to take care with your line for Joseph that you don't make a mistake by going off his line.
Possibly the date that you have for Joseph's parents from his papers relates to their marriage. There is this entry showing on the OPRs:
John Stewart and Janet MacNaughtan on 23/05/1824 in Dull, Perthshire
Have you looked at any of these original images on Scotlands People to see what they may say about the family? Going by the dates we are seeing, possible that parents moved to Edinburgh after their marriage in 1824 and first born Elizabeth born there.
Monica