So, your former spouse has proposed a property settlement that includes keeping you on the lease until December, correct?
Removing someone from a lease agreement is a bit of a painful process because it means breaking the lease and creating a new one. There's a few reasons your ex is probably looking to avoid this.
First, the landlord may refuse to sign a new lease where there is only one income supporting the rental payments, particularly if that income is low.
Second, if they did refuse a new lease, it means there will be a cost of breaking the old lease. I'm not sure exactly what this will be as it's governed by state law, but ordinarily, it's about four weeks rent and the cost of advertising for a new tenant. Your spouse might want you to pay those costs, or at least half of them, if this situation occurs.
Third, if they did agree to a new lease, they may impose a rent increase, like the solicitor said.
However, I also see your concern about staying on the lease - she may sting you later for half the rent, may not return your bond to you, may damage the property for which you'll be equally responsible, or it may affect your credit rating.
I always advise getting legal advice, mainly to check how a property settlement that precludes you from responsibility for the rental property interacts with state laws around lease agreements. It may be null and void when push comes to shove, but a Legal Aid solicitor can give you some guidance about this, and they offer free consultations.
Beyond that, though, perhaps you could consider agreeing to stay on the lease, maybe conditional on full and immediate repayment of your portion of the bond and exclusion by written agreement from all responsibility related to the rental tenancy. I think it would be wise, as well, to alert the real estate to the situation, so they will focus on her for the provision of rent if at any time it goes unpaid.
It's a dirty tactic, threatening to pursue other assets if you refuse the agreement, but I implore you to interpret such threats as just that - only threats, because in context, what's been threatened may not be all that crash hot in reality.
The court decides property settlements as follows:
1. What's the total value of the joint asset pool? In this case, it sounds like it might include furnishings, maybe a car and superannuation.
2. What's the financial and non-financial contribution of each party? Non-financial contribution is if she stayed home to keep house or care for the kids while you supported the family financially, but if there are no kids and both parties just worked, it'll be mostly financial.
3. What are the future needs of each party? Ordinarily, this raises questions about who will be caring for the kids, or if one person has a disability, etc.
4. Is the settlement just and equitable?
You've indicated that, realistically, the only asset you have is your superannuation, so let's look at that in context.
In property settlements, only the portion of superannuation earned during the marriage will be considered, so six years' worth. However, if your former spouse was also working for that six-year period and not raising your kids and the like, then you are also entitled to a portion of her superannuation in equal measure. It may be the case that one will cancel out the other, but even if that wasn't the case, the cost of pursuing a property settlement for superannuation will probably exceed what she stands to gain from it. Court isn't cheap, after all.
You've mentioned alimony, which isn't awarded in Australia anymore. The closest thing is spousal maintenance, and the court will only order that if the other party can show they will be exposed to financial hardship as a result of the separation. If she's able to pay the rent on her own, if there are no young children requiring care, and if she is, or has been, or is quite well able to work during your marriage, the court is unlikely to order the payment of spousal maintenance. It's not an order often made in this day and age.
Anyway, I hope this helps. Realistically, if you remove your name from the lease agreement, it will probably be you who foots the cost of doing so, but for her, going after other assets will probably be more fiscally detrimental than rewarding.