Do I need to prepay estimated taxes from 1099 income, if I didn't earn most of the income until after 10/01/18? Can I just file 2018 taxes and pay the liability then?

So I worked for a company from 1/1/18 through 8/1/18 as a W2 employee. I then left but did some part time consulting for them as a 1099. I billed and was paid for just over $70k, almost 75% of which after 10/1/18. I really don't know how to go about making any prepayment of estimated taxes for 2018, since it's already past at this point; wouldn't it just be better to file my taxes and pay the determined liability? I want to avoid any underpayment penalties or AMT, if they apply here.

If relevant to the timing, I will not be able to file taxes until early to mid april (K-1s that are frequently revised in February and March).