Small to big

[turf3]

Even rather tiny people play guitar with success.

Key is setup. Too many steel string guitars come from the shop with action unplayably high at the nut. There's absolutely no excuse for this but it persists. Even a cheap guitar can be made to play worlds better with a proper setup. You have to find a shop that's not caught up in guitar snobbery to get a good setup on a cheap guitar. I knew a guy but then I moved. My $200 guitars play better than many $2000 guitars.

[Michael N.]

No one should be intimidated when going from a Uke to a guitar. Of course it's much larger, the scale length much longer, the stretch much greater but I have the reverse issue i.e. going from a 'stretched' fretboard to one that feels cramped. You have to become accustomed to switching between the two, takes time but of course it's perfectly possible. I know someone who can switch between piano, guitar and violin without any issues at all, 2 minutes on each one played right after each other. He can only do this because he has practiced it.
I'm much more familiar with nylon classical guitars and the 'standard' scale length is 650 mm. That would feel mighty long to someone who has only ever played uke. It is possible to buy them in shorter scales and if you happen to have a small hand size it's not a bad idea to choose one that is less than 650mm. The other possibility is to buy a capo and place it on fret 3 or fret 4, move it down by one fret at a time as your hand and fingers become more accustomed to the longer stretch found on guitars. Don't forget that 12 year old kids can play full size guitar, sometimes to a pretty high level and 12 year olds don't always have the longest of fingers.
You can do it but give yourself time. Learn to relax into the stretch and minimise the tension. Easier said than done and not something that I find easy even after years of playing. That's me but then again I tense up at just the sight of any musical instrument!