I got the top tube, but that only measures to the middle of the headtube. To get total reach, you also need to add the stem length to it. If your Quick is sporting a (for example) 90mm stem, you could conceivably get a frame with a 52.5cm headtube and put a 70mm stem on it to get roughly the same fit.
Given your dimensions, you’ll definitely be looking at extra small bikes. I don’t think you need to go to 24″ kids bikes though. Most manufacturers do make very small bikes. I don’t know if you’re female or not, but the big manufacturers pretty much all have women-specific lines these days, which will usually have small sizes available. I know a few ladies in the 5′ range rocking regular 26″ mountain bikes.