I think that the first step you could do regardless of your decision to skip is to afterschool your child - no matter what. If you find the time or resources lacking, please consider a tutor or tutoring center that can meet the needs of your child in math and LA.
As for grade skipping, if I were you, I would save that skip for middle school and ask for subject acceleration and differentiation right now.
I have put my gifted 6 year old in a school that offers subject acceleration - but the accelerated math is still too easy for him (even when it is 2 years ahead of his age/grade) though the accelerated LA is at his level because they use real literature and literary analysis and there is no restriction for book choices. We consider that the math at school is "review" type math.
But the school offers other subjects which keep him happy all day long - like geography, history, computer programming, music etc where he does not get bored because he is learning things new to him.
So, we afterschool in math to meet him at his level and he reads higher grade level fiction and non-fiction at reading time in school where they let him bring in his own reading material.
