I have an almost 9 month old & I've been taking her to the gym & we walk on the treadmil while she is in the baby bjorn or when she was younger I had her in a sling. Also I have seen people put their baby in the carseat carrier next to them while they run whatever. I just asked at my gym & they said I could have her anywhere but the weight areas. Hope that helps!
Oh and I go to the Health and Athletic in Flower Mound and they take babies at 3 months.