Does anyone have experience with toddler constipation linked to a gluten sensitivity?

I had my three and a half year old in to the doctor for something unrelated this week and we saw a different doctor in the practice than we usually do. He was glancing back through her chart and saw lots of notes on her ongoing constipation, frequent complains of upset tummy, and very, very picky eating struggles and mentioned it as something to look into. We've been focusing on eliminating dairy, pushing fluids, fruits, fiber, whole grains, probiotics, etc. and gluten isn't something we've looked into so far.

We have an appointment with her regular doctor next week, but in the meantime I'm curious if anyone has experience with gluten making a difference or being a concern linked to constipation?