There doesn't seem to be a set amount that is paid, but $1200 is approximately in the ballpark, if maybe a little low.
Several sources online have given various different values for the amount paid out, and it seems to be determined on a number of factors.
From an article from justsecurity.org
In Kunduz, Afghanistan, where the U.S. military mistakenly bombed the MSF hospital in 2015, the amounts offered for the 42 deaths ($6,000 per claimant)
The average condolence payment under CERP (Commander's Emergency Response Program) is even lower—about $2,500—not because of a determination that this amount of money is adequate, but because $2,500 is the highest amount that a battalion commander can allocate on his/her own under CERP.
In 2015, CIVIC released a report documenting considerable discrepancies in payment allocations in Afghanistan from October 2005 to September 2014. For example, in Fiscal Year 2012, the death of two women prompted a payment of about $3,000; the death of a man, about $9,000; the death of a son, about $150; and the death of a daughter, about $5,000.
From an article from The Intercept
A child who died in a combat operation: $2,414.
Condolence payments are meant to be symbolic gestures, and today in Afghanistan, they are generally capped at $5,000, though greater amounts can be approved.
According to the data we received, in fiscal years 2011 through 2013, the military made 953 condolence payments totaling $2.7 million. $1.8 million of those were for deaths, and the average payment for a death was $3,426. Payments for injuries averaged $1,557.
From an article on The Atlantic
One record, obtained by the American Civil Liberties Union, authorizes $1,000 for "a Solatia payment for a lady whose son was killed by coalition forces." (NOTE: source provided a link to the document but the link appears to be broken as of 9/27/2019)
In 2006, soldiers fired on a taxi that did not slow down at a military checkpoint in Iraq, killing a woman inside. The military determined the checkpoint wasn't adequately marked, and her family received a large payment, of $7,500.
Today in Afghanistan, according to a Pentagon spokesman, condolence payments can be up to $5,000 for a death or injury, or $5,000 for property damage. Greater amounts can be approved in certain cases.
It doesn't appear that there is a set amount that the US pays per civilian killed, but instead pays out of a fund that does not have well defined rules as to how much it should pay out. It appears these funds may be set up automatically through the Executive Branch during times of military action beforehand.
From the same justsecurity.org article linked above
When President Barack Obama announced the air campaign against the Islamic State (ISIS) in August 2014, there was no framework for providing condolence payments in Iraq or Syria. The NDAA authorized the use of Commanders’ Emergency Response Program (CERP) funding for such payments in Iraq in November 2015 and Syria in December 2016, allowing up to $5 million for such payments. In their November 16, 2017, New York Times investigation, however, Khan and Gopal found that “the Defense Department has failed to enact these provisions or even propose a plan for how it might disburse that money.”