I followed Dr. Gross' protocol until about 4 months. I asked him for a script for PT at 4 months, which he provided, but stipulated strengthening ONLY.
My PT was really decent, and did not do any ROM stuff. But, I will say that the PT helped me make some real progress that I wasn't making by just walking and doing leg lifts. I would encourage it, but you might consider waiting a little while longer. That's just my $0.02.
For what it's worth, my wife's good friend is a PT. We visited them over New Year's, and I asked her a question. My groin gets sore when I run over 1/2 mile, and I have to stop. She suggested stability exercises (stand on just the operated leg and balance, one legged BOSU squats) to overcome that. You probably would not do the squats, but doing some balance exercises that isolate the operated hip could help.
In fact, when I WAS in PT, I was hooked up to the cable machine to do leg lifts (front, back, side, other side). When I did the NON-OPERATED hip, my new hip was forced to balance and hold the hip still when the other leg did the lifts. That made a huge difference. You might be able to do that with some latex exercise bands just as well (LIGHT weight).