thatbritishlass

Erin, I am so sorry for your loss. This is a really tough thing to go through and I can't imagine what you must be feeling.
Leenie correctly said that your daughter is automatically entitled to UK citizenship through British parentage. You can register the birth with the British Embassy but it is not obligatory. You can just apply directly for a passport. However as the British parent is now deceased you may wish to register the birth at the Embassy as it's a useful document for proving nationality. Website is: http://ukinusa.fco.gov.uk/en/help-for-british-nationals/living-in-usa/birth-registration/
You don't have to do any of this right now. Take your time, give yourself some time.

Hi guys.....I got approved today!!!!
LONG wait at the embassy but really really positive experience (much better than my 2 previous visits as a non-immigrant visa applicant!!) - at the end of my 90 second interview the CO congratulated me and welcomed me to the family
High as a kite...spent a great afternoon in London afterwards with my best friend/maid of honour...just got back to Leeds now and absolutely WIPED but wanted to spread the good news!!