What you propose is to convert unsecured debt into secured debt. Conversion of unsecured debt into secured debt is not generally a good idea (several reasons). The debt you currently owe does not have assets securing the debt, so the creditor knows they are exposed to risk, and may be more willing to negotiate or relax terms on the debt, should you encounter problems. When you provide an asset to secure debt, you lose freedom to sell that asset. When you incur debt their is usually a spending problem that needs to be corrected, which is typically not fixed when a refinance solution is used. You do not mention interest rate, which would be one benefit to conversion of unsecured to secured debt, so you probably are not gaining adequate benefit from the conversion strategy.
This strategy is often contemplated using 'cash-out' refinancing to borrow against a home you already own, and the (claimed) benefit is often to lower the interest rate on the debt. Your scenario is more complicated in that you have not purchased the home (yet). Though it may be a good idea to purchase a home, that choice depends on a different set of considerations (children, job stability, rental vs. buy costs, lifestyle, expected appreciation, etc) from how to best handle a large debt (income vs. expenses, how to increase income or reduce expenses, lifestyle, priorities, etc).
Another consideration is that you already have a problem with the large debt owed to one (set of) creditor(s), and you have a plan which would shift the risk/exposure to another (set of) creditor(s) who may have been less complicit in accruing the original debt. Was the debt incurred jointly during the marriage, and something you accepted responsibility to repay?
You mention that you make great income, and you specify one expense (rent), but you neither provided the amount of income, total of all your expenses, nor your free cash flow amount, nor any indication of percentages spent on rent, essential expenses, lifestyle, nor amount available to retire debt. Since you did not provide specifics, we can take a look at three scenarios,
scenario #1, $4000/month income
rent $1500/month (37% of income)
essentials $ 800/month (20%, utils, food, transportation)
lifestyle $ 800/month (20%, clothes, entertainment, cellphone, etc)
remainder $ 900/month (23%, save, pay debt, etc)
scenario #1, $6000/month income
rent $1500/month (25% of income)
essentials $ 900/month (15%, utils, food, transportation)
lifestyle $1200/month (20%, clothes, entertainment, cellphone, etc)
remainder $2400/month (40%, available to save, pay debt, etc)
scenario #1, $8000/month income
rent $1500/month (19% of income)
essentials $1200/month (15%, utils, food, transportation)
lifestyle $1200/month (15%, clothes, entertainment, cellphone, etc)
remainder $4100/month (>50% available to save, pay debt, etc)
Depending upon your income and choices, you might have < $500/month to pay towards debt, or as much as $3000/month to pay towards debt, and depending upon interest rate (which OP did not provide), this debt could take < 2 years to pay or > 5 years to pay.
Have you accepted the responsibility for the debt? It will be a tough task to repay the debt. And you will learn that debt comes with a cost as you repay it. One problem people often encounter when they refinance debt is they have not changed the habits which produced the debt. So they often continue their spending habits and incur new unsecured debt, landing them back in the same problem position, but with the increased secured debt combined with additional new unsecured debt. Challenge yourself to repay a specific portion of the debt in a specific time, and consider ways to reduce your expenses (and/or increase your income) to provide more money to repay the debt quicker.
As you also did not disclose your assets, it is hard to know whether you could repay a portion of the debt from assets you already own. It makes sense to sell assets that have a low (or zero) return to repay debt that has a high interest rate. Perhaps you have substantial assets that you are reluctant to sell, but that you could sell to repay a large part of the debt?