Hello. 9x19mm is generally not considered adequate for anything larger than small to medium game but assuming the following, it will work for quick, humane kills:
1. Size of deer. (Here in Texas, whitetails are not the monsters they can be farther north)
2. Load Selection (I like the 124 XTP @ 1250 ft/sec)
3. Skill of shooter. (Must be able NOT to just hit the deer, but pick the place where the bullet will do what's needed and hit that)
4. Limit distance (I will not shoot past 35 to 40 yards assuming that all conditions are perfect. Most of the time I am within 15 to 20 yards.)
5. Be willing to pass more shots than you take.
I have consistently had good luck with Hornady 124-gr. XTP over 6.0-gr. Unique out of a Hi Power or STI Trojan 6" Long Slide.
These are the same criteria I self-impose when using .38 Super or .45 ACP as well.
The 9mm load mentioned has completely penetrated 3 deer broadside, one being through both shoulders.
I have not used the Gold Dot in any weight. Years ago I cleanly killed deer with broadside shots using the Sierra 115-gr. JHC but only on broadside shots. Where the XTP has always completely penetrated deer for me, the Sierra bullet never did. Recovered bullets were like little flattened lead pancakes and some fragmentation was evident.