Full disclosure:I make some of my living from teaching people how to play the ukulele. Not kids as a rule, and not generally beginners.
It depends on the kid, of course, but I think there are various types of ukulele depending on what she likes, and how much time you are willing to spend with her.
She can start off with any of the cheapo wooden ones and these are fine if you pick a good one but about 10% of them are completely unplayable. As a guitarist, you will be able to spot an unplayable one as it will be like an unplayable guitar.
If you can't find one secondhand, I like these Junior Rockstar ones at Smyths Toys:
https://www.smythstoys.com/uk/en-gb/toys/arts-crafts-and-music/musical-instruments-and-karaoke/musical-instruments/rockstar-ukulele-junior-pink-50cm/p/168154
Because they're moulded plastic they're totally reliable and all have perfect intonation and action, as well as being very tough. They need a lot of tuning (the tuners are awful but they do work) and if you ever leave them in a car on a hot day you'll find they melt - when you take them out of the car the action will most likely be about an inch at the 12th fret!
If you are near Derby I have a nice purple one that you can have for the £2.50 I paid for it in a charity shop.