Christi, you need to start by getting their Australian certificates which are usually very informative - far more so than IoM ones. e.g. NSW death certs have parents' names and addresses, how long the person has been in NSW, as well as a lot of other information.
The more you can do before you go to the IoM, the more you will find there.

You should work backwards from the earliest person in your family whose dates (birth & marriage) you are certain about. First their birth cert., then their parents' marriage cert (from details on the birth cert.) Then the parent's birth cert. from details on the marriage cert., and so-on, until you get back to the Edwards sister who was your ancestor. Then her marriage and death certs which will give you the information you need for her shipping record, and to be certain of her ancestry in the IoM.
No point guessing, if you want the right person!

Sue