Yes, Park House has a good reputation. Some schools in Doha are more "British" than others and "English-speaking" can mean just about anything.

The horrors of school waiting lists has been a perennial topic on this forum. Alas, the indications are that the problem is getting worse, not better. There are still schools that will not even give your child a place on the waiting list, never mind an actual place at the school!

For many schools, it helps if you have a British passport and heaps of cash. However, with many of the better schools being hopelessly oversubscribed, the temptation to put up the school fees yet again is almost irresistible.