Honestly, I haven't. But after some research, I come across this case series of seven patients with new-onset psoriasis after getting the mRNA vaccine, of which six occurs after the second dose and one case after both the first and second dose:

https://www.jaadcasereports.org/article/S2352-5126(21)00862-6/fulltext

The only case (1 out of 7) who got psoriasis twice after each mRNA vaccine dose was a 52-year-old female.

I haven't heard of psoriasis cases after DNA vaccine. Is it not possible for your daughter to pick another type of Covid-19 vaccine?