Yes you do. With that type of time you should have a shot to go anywhere you want. Are you looking at a specific company?

From what I see you are an F/O , the JAA conversion is not as tough as doing it from 0 hours but it takes time.

You have two options:
Distance Learning or Full-Time learning.

Distance Learning can be done from your home but most schools require you to go there for a brush up (1-2 weeks) before you give the exams. This might be a little difficult, unless your airline can give you the time off. Distance Learning can be done a soon as 7 months or it can go for a year, it all depends on how much studying you do, and trust me it's a lot.

Full-Time is more structured, should last 6 months. You will be in a classroom for about 600 hours and be done in the quickest time.

THIS IS THE FIRST STEP. After that you will need to convert your CPL/IR (15 hours minimum of flighttime)