Take your time with dating. You need to heal from your marriage AND figure out how not to repeat the pattern in a new relationship - it takes a while to digest that.
And please, please, please do NOT involve your daughter in your dating. 6 months of dating should be a MINIMUM requirement before they meet your daughter - and then only if you think the relationship will likely become permanent. Kids get attached and then suffer the pain when the relationships break up.
You're going to be ok. Be frugal and make wise financial choices because you have your financial security in retirement to think about as well as the costs of raising a child. Good books to read are Your Money or Your Life by Dominguez and the Tightwad Gazette books.
I'm glad there's an older child in the nanny share, that gives you more security as she would be likely to speak up if anything was awry. Congratulations on getting back into work in your profession. I know you're facing a lot of challenges but you got this.