I am seeing about 140 to 150fps increase when going from a Glock 19 to one of my PSA AR 9s with 16" barrels. This is using my handloads using Alliant Sport Pistol and a 147gr grooveless coated cast bullet. With Speer Lawman 115gr TMJ I am seeing almost a 340fps gain at 1500fps out of the AR 9s. Velocity increase will very greatly based on the burn rate of the powder as well as other factors. I believe Speer uses BE-86 in the Lawman loads so that will give a much larger increase in speed with the longer barrel.
I haven't chronographed the Speer 115gr Gold Dot load in the AR 9, but in a Glock 19 it averaged 1230fps when I tested. I would believe it would therefore average around 1570 or so out of one of my 16" barreled ARs. Using a ballistics calculator and Speers data for the BC, that bullet would be traveling at about 1155fps at 100 yards. Near the muzzle, I would be concerned with it being way over driven. I am going to test it here shortly with water jugs to see if it will hold together at all. I'll test that more out of curiosity than anything.
I think a better choice would be a 147gr HST, Gold Dot, or 135gr Critical Duty. The Critical Duty will probably gain the least in velocity and that bullet will hold together when over driven.
With a 147gr Gold Dot, it should be easy to achieve 1100fps. Using that velocity and Speer's BC figures, it would be doing about 959 fps at 100 yards.