Doha British School used to be called Doha Montessori. Don't know why it changed its name, but it seems to be highly regarded among Brits.
DESS and Doha College are both excellent but hellishly difficult to get into, and constantly over-subscribed except in the upper senior years, when many kids get sent back to board in the UK. They are sponsored by the UK government and Brits who are sent to Doha in a government capacity or posted there by British companies get first dibs on places.
Compass - extremely good but expensive, though they are expanding and building a new campus space should not be an issue. Yet to prove themselves results wise though, as they are just taking there first lot of seniors through GCSE.
Sherbourne - pretty much everything I said about Compass also applies to Sherbourne, though they are a very different animal in terms of ethos and style of teaching.
Park House - also highly regarded by Brits. Tends to be full up at the lower end, with spaces at the upper end, same as Doha College.
If you are applying to DESS, Doha College, Sherbourne and PH your child will need to sit an aptitude test in maths and English. If they don't pass they don't get in. Simple. And the pass rate is quite high.
Compass do test, but only to get the measue of the level of your child - they do not select purely on ability and are much more inclusive in that respect.
I think DBS do test, but not sure how tough it is.
There are other schools that call themselves 'British Curriculum schools' but to be honest they are rarely anyone's first choice - though they are sometimes the only choice. 
It's very tough indeed. Be prepared for some stress!