Be careful if it's a fluffy polyester batting. If your ties are far apart, it probably won't hold up in the wash. Quilts for 3yo tend to get regular brutal washing and drying, which can cause batting to "ball up" and get lumpy.
I'm thinking you would be better off with Warm n Natural -- a very sturdy batting (because it is needlepunched through scrim) that can be tied up to maybe 10" apart and still hold up well in the wash. I would think a fluffy poly batting would require ties every 2" to 3" in order to hold up well over time.
Do you still have the batting packaging? It should say on there how closely the batting needs to be quilted. That would be the max distance for ties, I think.