I pull my 4500 comfortably with a vw jetta, something funny is going on if you're getting that much bucking. I wouldn't jump straight to replacing axles tho, start with the cheap/easy stuff.
I'd go tow vehicle back,
1) is the receiver hitch tight on the tow vehicle? (i used to have one that would move making noises that sounded way worst than they should have)
2) is the ball the right size for the trailer?
3) is the coupler adjusted properly for the ball
4) do you have enough tongue weight
? (mine pulls better with a battery
5) tire pressure? free to check
6) suspension condition
7) Frame condition