Congrats on your win, and welcome to the addictive world of chickens
May pullets usually start laing in October. 5-6 months is a good rule of thumb for most breeds.
Keep in mind also, most of your birds aren't high production breeds.They may take a bit longer than say Rocks, sex links, Australorps, etc. The Delaware could be the first to start laying. I'm not too familiar with Buttercups, so I don't know how fast they mature. Brahmas can be pretty slow to mature, so you might be looking at 7 months or so for her. I don't think speckled Sussex come in bantam? So I'm guessing you have an OEGB. You can also tell from teh body type--Sussex are pretty heavy bodied, games are light with downswept wings. Post a pic, and we can help you ID her.