Firstly, the burial record is on the National Burial Index. Buried 13th Feb 1840, aged 44, assumed born around 1796, St Mary & St Laurence Church Great Waltham. The Death registration is 1st Quater 1840, Chelmsford. You can obtain copies of the original certificate, online, from http://www.gro.gov.uk/gro/content/certificates/http://www.gro.gov.uk/gro/content/certificates/ But I don't think they give parents names. They state the date of death, the cause, together with the deceaced's occupation, and age. The person who reported the death is shown.
I have no direct access to Waltham Parish Records. Many such records are on the IGI index, but I can find none relevant, so cannot comment on any birth records for the children etc. All I am going on is my own records which attempt to "reconcile" every Stock on every census from 1841 to 1901. The 1841 census is very consistent with the information you supplied. We have the family headed by Lucy age around 35, with children George, 6, Peter, 5, Moses 4, and Aaron, 1. Census data is often "approximate", but my instincts would say that to have been put down as aged "1" in early June 1841, all we can assume is that he probably had not reached his second birthday, and was therefore perhaps born after June 1839 onwards.
The only registered birth in UK, pre-1841 is Aaron Stock registered Chelmsford 4th Quarter 1839, Volume 12 Page 40. Ordering the certificate from the above source would confirm parent details - usually with maiden name of mother. In my own records, I have "attached" this birth to the census record since they are highly consistent. An advantage is that Aaron is far from being the most popular name in those days.
Of course I don't know the source of the other information, but you are suspicious about the 8/9 month gap. However, since birth registrations only came in halfway through 1837 (and not every birth WAS registered then), I assume the information derived from parish (church) records. These, typically, would record BAPTISM dates and my experience says that baptisms then followed no strict pattern. Some of my own ancestors were not baptised until the age of three. However, I agree with one major inconsistency in that he couldn't possibly have been baptised November 1836 if he wasn't born until Q4 1839. But don't rule out bad transcriptions or difficult reading of (microfilmed) parish records where often letters and numbers are genuinely misinterpreted.
The IGI index show TWO George Stocks born around the "right" time. I personally had been driven by the burial record (indicating birth around 1896). I had tied this in with the record showing (in this case it DOES show the birth date, not baptism date) George Stock born to William Stock and Mary Boltwood on 8th December 1794.
There is also an entry for George Stock being christened on 5th July with parents William Stock and Elizabeth (surname unknown). The latter record comes from a "Batch Number" (C043191) - which would purport to be a proper transcript of the parish records. The record I am going on is "reported" to LDS. Such reported records are occasionally very accurate, and occasionally total rubbish. So it's difficult to say either way.
If this were my own family, I would try to resolve it by looking at the original parish records at Chelmsford Records Office. [There could still be hypothetically reconciling factors - for example a birth in 1794 to William Stock and Mary Boltwood. Possibly Mary died in childbirth. William could have re-married an Elizabeth who then suggested having young George baptised at 6 years old. But I'm just making that up as an illustration].
I think this summarised all I know and all I can suggest at this stage.