Not sure why you think that Peaches is going to double clutch but ... 1) first clutch April first ... 2) she seems to be going into shed (?) ... 3) it will take "x" amount of days to shed ... 4) if she is going to lay, the eggs will be laid approx. 10 days - 2 weeks (give or take) after shedding.
So, if she is just going into (or is in) blue, and given the time it takes to shed & lay eggs, it may be possible that Peaches will double clutch, as you say, "that fast".
Double clutching is harder on females who are "rail thin" from their first clutch. I cannot tell you if Peaches will be okay because I do not know her condition & other factors ... nor am I psychic.

However, if she is in good health, has been eating since laying the first clutch, etc. ... I would venture a guess in saying that Peaches should be okay if she double clutches.