Hi Francois - first, welcome to WikiTree!
Second, I think I've found Peter Fraser in the records of PRDH and the Drouin Institute - and good to confirm they also covered Scottish immigrants reasonably well:
FRASER - Pierre, Peter, Pitre / Immigrant / Born about 1761 at Inverness, Scotland to parents Alexander Fraser and his wife Mary.
Among original records, it's clear that Peter married on 14 March 1801 at Saint Andrew's Presbyterian Church in Quebec to Josepte Chasse. The original act is also available at Drouin IGD and potentially elsewhere (although I didn't easily find him on FamilySearch).
Peter was noted as being 40 at the time of their marriage and his wife 25. He signs as Peter Fraser and his wife as Josepte Chassé.
Their marriage was noted as being "by license from His Excellency Governor Milnes." Sir Robert Shore Milnes was the British Lieutenant Governor of Lower Canada from 1799 to 1805: https://en.wikipedia.org/wiki/Sir_Robert_Milnes,_1st_Baronet
The names of Peter's parents are not referred to on his marriage record, but (per PRDH) came from a marriage contract of 13 March 1801 before the notary Alexandre Dumas.
IGD re marriage: https://www.genealogiequebec.com/Membership/LAFRANCE/acte/5405131
I hope that's helpful and you now have some docs to explore..!