You can start the immigration process and take the exam later but it's advised that you take it before.
The reason for that is that when you estimate your points, before taking IELTS, you don't know how many points you will get. It could easily happen and has happened to many people who have been on this forum that once you are asked for your documents and IELTS and have 120 days to send them, you finally take your IELTS but the results are not as good as you'd hoped for and you end up with a total of less than 67 points. Since most places do not have IELTS tests scheduled every day as well as dates may be filled up, you might have time to repeat the test within the 120 days if you are lucky but again, the results of the second one might still not give you enough points.
So.. if you don't need any points for English or you are very sure of doing well on IELTS, take it later. Otherwise, take it before you apply.
