If a character spends their action to Dodge, then moves away from an enemy within 5ft. Would the enemy roll his opportunity attack with disadvantage?

I've never thought about this until today.

I just wanted to be sure just in case it comes up in a game. You know, seems the kind of too obvious, absurd, but true type of rule :)

Seems legitimate - the wording of Dodge is 'until the start of your next turn'.  It only applies 'if you can see the attacker' but strafing/backpedaling to begin with is a thing. 

I never knew that, this is great.

Half way through a session this evening with my Barbarian. Broke through a barn wall with my great axe, rage, run forward at thugs, miss, hit, crit, then thought what can I do with dodge. Then I thought hey. D&D Beyond has a community to answers these things. Thats +1 for Curse.

Well you could also disengage, but that only helps you avoid opportunity attacks. But yes, dodge action then move, you have a better chance avoiding opportunity attacks (but not a confirmed success like disengage), but you then are safer from any normal attacks up until the start of your next turn.

Depends how you want to play it - confirmed safety vs. long disadvantage against you.