You can do both simultaneously. You can obtain Univ. transcripts and send it to WES and at the same time you can prepare for IELTS. So within 3 months, you can obtain ECA report and IELTS test report.
you should book your Ielts test date ASAP, as mostly you ll get a test date with a gap of 30-45 days may be more from the day you book. Hence you ll have ample of time to prepare in between. Meanwhile simultaneously you should immediately apply for WES, as it's a maximum 45 days process, which includes 20-25 days for your University to issue your trancripts and have them sent to WES, and then 20 business days taken by WES to evaluate your credentials and issue a report. WES does not need much effort from you. you need to create a profile online pay fee online and one day to go to your university and get your transcripts. Rest all you have to do is wait.
Hence my advice, do both simultaneously and approximately within 45-50 days you ll have both results in hand. All the best.