Most of the parish of Alyth is in Perthshire. The old records are arranged by parish, so even if a place is in the Angus bit of Alyth, it will be in the records under Perthshire.
In 1975, when counties were abolished as local government units, Alyth became part of Perth and Kinross District. There is no 'county of Perth and Kinross'.
In the IGI,
anything 'submitted' is automatically suspect unless there is a matching 'extracted' entry, because you don't know whether it has been generated by good research or by someone's imagination or wishful thinking (or worse!). In this case there is an 'extracted' entry for the marriage so that can be regarded as reasonably reliable, and you should be able to find and check the original marriage entry at
www.scotlandspeople.gov.uk.
It's not immediately obvious where William's and Janet's 'submitted' birthplaces and dates of birth came from. It can't be the 1841 census, because the 1841 didn't list birthplaces. It could be the 1851 or later.
Bear in mind that the census is usually taken about the end of March/beginning of April. So anyone born between census day and the end of the year will not yet have had their birthday in census year, and will therefore appear as a year younger than they would if the census were taken on the last day of the year. So if, for the sake of argument, Janet was listed as aged 40 in the 1851 census (and assuming that the information is accurate, which isn't necessarily so) she would have been born between early April 1810 and late March 1811.
Calculating a date of birth by subtracting the age from the census year will produce the wrong birth year for about 3 out of 4 people!
I agree with
ev that your next step is to find Janet's death certificate, assuming that she died in Scotland after 1855.