That 6hp should push you around ok.
I doubt if it will get the boat on plane though.
I've got a Johnson 8Hp on my 12 footer and it will get it on plane, but not by a lot.
Here's my dad (in his better days) planing it across the harbor:
Your 'rude is the same as my Johnson. Same family that is. Mine just has another 2 hp.
At 6hp, 14 feet, 2 adults and 2 kids you're probably going to push water.
Still, for putting around with the kids and the missus on a lake, it'll be fine.
Make sure you have oars just in case.
Is your transom sitting on the trailer supports or is it just above them? It looks like your transom is unsupported in the pictures on that trailer.
If it isn't touching, you're going to want to adjust them so they hold the transom.
while it won't fall apart today )or even tomorrow), an unsupported transom can eventually damage the hull while sitting on the trailer.
All the weight of the outboard comes down on it and the road bumps/vibration just makes it worse....