In a common core aligned school, a skip of 2nd, 3rd, 4th grade math is not so much a big deal. It's primarily calculation and getting fluent in math facts. 5th grade is primarily about fractions and longer calculations (more digits). 6th grade is intoducing ratio, percent, proportion. 7th - 8th is prealgebra and pregeometry.
My son skipped 2nd, 3rd, most of 4th grade math, no gaps observed and no difficulty with higher math grades. His best friend skipped 3rd and 4th grades and has no problems in math.
Algebra can be taught very early. I mean, it already IS taught early. It first shows up as "number families". Like 2 + __ = 5, 5 - 3 = __ When my son was little, he struggled with math fact recall because of his slow processing speed. I would make up handwritten worksheets about "Mysterious Mr. X". I had made up a whole elaborate character Mr. X. to explain variables. I would disguise practicing times table facts as fact family style prealgebra to keep my son interested. 56 = 7X, for example.
With that said, if it's not broke, don't fix it. Teaching math can put pressure on a situation. Math is difficult to differentiate. If the school doesn't support subject acceleration, what options remain? How far can she accelerate without negative effects? Does she even enjoy math? Is she satisfied in math class? If she is doing well socially and emotionally, acceleration may create more trouble than it's worth. If she is frustrated, bored, acting out, feeling misfit, that's the type of situation where accelerations (not just grade skipping, but any form of acceleration) may make a big difference.
My son ended up accelerated further in math because it's the easiest subject to measure. Turns out he hates math, but even homeschool law in my state requires him to continue sequential instruction, so poor kid is going to sit through a lot of complicated math.
