Could I please clarify something? Are you moving away from your SISTER in order to improve your family life.. for example she is one of the reasons your family life needs improving. Or are you saying you are moving to Perth to improve your life as where you are LIVING is causing problems, which just happens to be away from your sister?
This is your situation and your sister but putting myself in your shoes, this is how I would handle it personally. If my 16 year old sister told me she was pregnant I would take a lot of things in to consideration.
For example... Does she want the baby? (I don't believe in abortion but I do believe in other people's freedom of choice, so what I do and other people do are different and I respect it. An example being my best friend had an abortion and I wondered silently how on Earth she could do it but held my tongue and supported her with HER decision as her choices do not belong to me).
How long has she been with the boyfriend?
How mature is your sister?
Does she work?
How mature is the boyfriend?
Would he make a good father (these are your sister's choices, not yours remember. Example being, my family HATE my partner and believe he is wrong for me. However in my eyes he is the best thing that has ever happened to me and is a WONDERFUL father.)
Does your sister believe she will be a good mother?
Does she think her boyfriend treats her well enough to support her and a family?
Is her partner working?
If not, is he willing to work?
What is her plan?
What is his plan?
What is the backup plan?
What is their budget?
What support is available from any family support services such as Centrelink and Family Tax Benefits?
Can she access a health care card?
And so forth. I think if you sit down with your sister and ask her these kinds of questions, she will be able to come up with the answers she thinks is best for her. Based upon the answers of your sister, you can then work around and come to conclusions, she is happy with and so you also have a plan and know where you stand.