As I remember, the Treaty of Ghent allowed for the time it would take for news to reach different parts of the world and so set different dates for the cession of hostilities in different regions of the oceans.
ARTICLE THE SECOND.
Immediately after the ratifications of this Treaty by both parties as hereinafter mentioned, orders shall be sent to the Armies, Squadrons, Officers, Subjects, and Citizens of the two Powers to cease from all hostilities: and to prevent all causes of complaint which might arise on account of the prizes which may be taken at sea after the said Ratifications of this Treaty, it is reciprocally agreed that all vessels and effects which may be taken after the space of twelve days from the said Ratifications upon all parts of the Coast of North America from the Latitude of twenty three degrees North to the Latitude of fifty degrees North, and as far Eastward in the Atlantic Ocean as the thirty sixth degree of West Longitude from the Meridian of Greenwich, shall be restored on each side:-that the time shall be thirty days in all other parts of the Atlantic Ocean North of the Equinoctial Line or Equator:-and the same time for the British and Irish Channels, for the Gulf of Mexico, and all parts of the West Indies:-forty days for the North Seas for the Baltic, and for all parts of the Mediterranean-sixty days for the Atlantic Ocean South of the Equator as far as the Latitude of the Cape of Good Hope.- ninety days for every other part of the world South of the Equator, and one hundred and twenty days for all other parts of the world without exception.
The treaty of Ghent was signed 24 December 1814 and was ratified by the US senate 16 February 1815. President Madison exchanged ratification papers in Washington DC 17 February 1815 and the treaty was proclaimed 18 February 1815.
February 16, 17, and 18 were the 47th, 48th, and 49th days of 1815. 90 days later would be the 137th, 138th and 139th days of 1815 - May 17, 18, 19 - and 120 days later would be the 167th, 168th, and 169th days of 1815 - June 16, 17, and 18. The battle between Peacock and Nautilus on 30 June 1815 was on the 181st day of 1815.
So obviously the course of the Peacock in April, May, and June 1815 would indicate how likely it was to have have heard news of the peace treaty by June 30, 1815, and whether the US government made sufficient effort to inform Warrington of the treaty.