I would commend the entirety of this chapter to you, as it is a psalm of praise to God for His deliverance of David from his enemies, and from King Saul, another enemy for practical purposes. the imagery David uses, the word pictures, really communicate what God did, and what he could do with God's help.
The image of the deer is just one David employs. Deer can fly. Thinking of sports, speed afoot is a great asset. In football, a fast player is an asset on both offense and defense. God gave David both offensive and defensive ability -- to fight and flee.
Deer are also surefooted. Have you ever seen one stumble? David was able to be stand firm amid attacks, both head-on and covert. He was able to hatch and carry out his own plans, standing solidly in his faith in God.
Deer are also agile and graceful. In our daily circumstances, let's be deer-like.
I Lift My Eyes Up (Psalm 121) - Brian Doerksen