mechanics of attack and roll damage for hill dwarf figther lvl1 [duplicate]

STR 13 +1
DEX 14 +2
CON 17 +4
INT 15 +2
WIS 12 +1
CHAR 17 +3

so I attack with one hand Battleaxe 1d8 with dueling fighting style:

  1. Attack rolld20 – 16+1 from strength +2 from proficiency with Battleaxe total 19
  2. Now roll for damage – 1d8 + 2 damage from dueling style = rolled 3+2 (dueling)

Is this correct? And on the attack roll do I need to add +1 damage from strength ability score modifier?