Turnip roots can be harvested any time you have something big enough to eat. Walnut sized roots are so tender and sweet. I can never wait for them to get bigger before sampling. I am told the greens can be steamed, but have never done that. The darn bugs love them and they always look like thay have been shot with a shotgun with very small shot. IOW they never look too apealing.
Turnips will get quite large, but the large ones are not as tender as the smaller ones. 2 inches diameter or smaller is about right for very tender roots..
Also, I will mention that if your turnips are not too crowded they will make good roots sooner. This is pretty much the case for all the root crops. If you want a 2 inch root, you need at least 2 inches between plants. 3 inches would be better. Thin them and use the greens.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-