In August I have my annual visa application in Chiang Mai.

My passport is valid until April 2012.

Should I first get a new passport or can I apply with my current passport and get a new passport in April.

You can get the extension of stay without problem.

They will give you an extension of stay till the date your passport expires. You return to immigration before that date with a new passport in April. At that time immigration will transfer your details to the new passport and also give you the rest of your 1 year extension (till Aug. 2012) for free.

Get your extension as required then apply for a new passport just before the old one is due to expire, then get the extension stamp transferred to your new passport, means visiting Immigration twice.

Get new passport now, do the extension when you receive the new passport, means one visit to Immigration.

Up to you but extension will only be valid up to April in current passport - after new one obtained full time would be allowed. But you need at least six months validity to travel most places so it would make more sense in my mind to obtain a new passport now, before you extend.