First off, the decision about marriage should be first and foremost about what is best for the both of you personally, rather than financially.
That said, my guess is that it's not in your financial interest to get married sooner, though you should look into it in more detail. Marriage has different effects financially depending on the differences between the two of your income levels. You should enter your current information into an online tax calculator and see what the difference is.
Two people with identical incomes, both going from Single to Married-Filing Jointly, would have similar taxes to before, if they are in the middle of the income brackets (say, $90k to $150k combined). Up to that point, there's not much of a difference. If you're at the low end or the high end, though, you may pay more in taxes if you have similar incomes, because at the high end the brackets aren't double for married-filing jointly, and at the low end you lose out on some things like Earned Income Tax Credit which for two children would have a maximum of $44k for single but only $50k joint.
Meanwhile, if you have disparate incomes, you could be advantaged OR disadvantaged, again depending on how things work out. If the income earned by each party is enough that neither of you can earn the EITC, and one of you is taxed at a higher marginal rate than the other, getting married effectively moves some of that money from the higher rate to the lower. For example, if one party has $105k taxable income and the other has $45k, the $105k party is paying 28% tax on the last $15k or so; married, you combine for $150k, which means you pay 28% on almost none of it.
This excellent Tax foundation article, Understanding the Marriage Penalty and Marriage Bonus, goes into a lot of detail on both sides of the issue, and has some good charts that might be helpful.
In your case, you don't list actual dollar amounts, but you say your fiancée gets about $8500 back; that makes me wonder if she's earning the EITC.
One other consideration is that, filing as Single-Head of Household, she gets almost $3000 extra tax-free income. You'll lose that extra exclusion when you get married; you'll get around $6k now and she gets $9k for a combined $15k exclusion, plus she gets higher income brackets all the way up even beyond the normal Single levels. So you'll be giving up $3000 times your marginal rate, and possibly more, if you get married. This doesn't mean it's impossible getting married now isn't a benefit; it just makes it less likely.
With the numbers you've added to the OP, it seems like you're better off waiting. She's getting $3k or so from the EITC, and if you get married you will lose all of that money, plus pay a bit more in taxes if she does qualify for Head of Household. I would recommend verifying that she does qualify for Head of Household, and not claiming it if she doesn't (as it would be a lie and risk being audited and having significant penalties), but regardless of that outcome the EITC by itself likely outweighs any other consideration. She also should strongly consider reducing her tax withholding if she's getting $8500 back; even ignoring the EITC and the refundable child credits, that implies she's still having thousands withheld from her paychecks that shouldn't be, giving the IRS a interest free loan.