
I would expect a medium size breed like my own to reach within hakf inch of adult height by 9 months old, after that they may add a half inch but they will mostly then develop more mass.
I kept tabs on my last pup out of interest (her Dads sires owner had a throry of what height pups should be at various stages to reach correct height by maturity) who is now nerly 20 inches tall, and she was 15 inches at 4 months and 18 inches tall at 6 months and 19 1/2 by 9 or 10 months.