I found data for a 1.05 kVA transformer for 60 Hz power. The efficiency is 94.7%, the core loss 22.6 W and the copper loss 37.4 W. That should give you something to work with.
The width of the transformer core is given as 2-1/8 inches. The thickness of the stack is not given, but in another table of data, most of the cores are square. The maximum flux density is given as 14.8 kilogauss (1.48 Tesla).
Other information from table:
Lamination: EI 212
Area product (core area x window area): 15.3
Current density: 1550 A/sq. in.
Copper regulation: 3.6%
Iron weight: 14.2 lbs.
Copper weight: 5.18 lbs.
Lamination: 29-Gauge, grain oriented (M6) silicon steel
Exciting VA / Input VA 23.5% for EI 625, 9.1 VA, 12.7% for EI 251, 3551 VA
Operating temperature = 75C (amb) + 75C (rise) = 150C
Information is from Nathan A. Grossner, Transformers for Electronic Circuits, McGraw Hill 1967 wit source listed as Electro-Technol., vol 67, no. 1, p. 61, January 1961, Copyright C-M Technical Publications Corp., 1961
Here are the lamination dimensions from Lamination Specialties Corp.