48-51cm frame, single speed

Wanting to build up a nice wee bike for my gf for her birthday in June.
After a nice and light frame to suit 5'6" rider.

Full builds or F&F considered.
Needs to take rear and front brakes.

I’ve got a brand new (still wrapped) Holdsworth (PX) La Quelda step through that I bought for my partner and never got round to building.

One of these:

Has had a headset/seatpost put in it and nowt else, frame still has foam tubes on it. Might be the right thing, might not, depends what kind of riding you see g/f doing. Any good?

https://www.lfgss.com/conversations/394138/#comment17345711

Thanks, I've now bought a Surly frame that popped up in eBay finds. I'll close the thread