I train my beginners on a short and wide kayak,. the WS Mallard being the best as it is stable and easy to paddle.
Once they get used to paddling and some experience and confidence, I move them up to longer and narrower and faster boats.
Shawna now paddles a Perception Carolina-145 but tells people that had I put her in that kayak to learn, she would have instantly given up the sport.
Being in a more stable boat let her learn without being scared.
@RikJohnson
Reason for my recommendation was that it sounds like the OPer has already had the time needed to get fundamentally used being on the water in a shorter, wider kayak. Granted a beginner in terms of specific skills, doesn’t sound like it is so in seat time. And at her size, she can go pretty small before a boat will feel as insecure as for the average sized paddler. Also not sure that starting off with a story about a kayak being scary is the right approach for this particular individual… the width issue is not what seems to be stopping her from the less wide boats, it is more weight and cost.
Hi RikJohnson & Celia, to clarify, with my small size & short reach, paddling a wider boat is very awkward- in a short, wide kayak (Riot Quest) I had to lean side to side just to paddle without scraping the side of the boat (terrible form, I know). Moving up to the larger (but narrower) Enduro was soooo much much more comfortable, not scary at all. Slightly narrower would be even better. Never had stability issues with either.
I’m still looking in the 12-14’ range (much longer could be a transport and storage issue, and I would question maneuverability on the odd river trip). Cost is also a factor, I’d rather a well made, durable 13’ that handles well than a longer boat that doesn’t track or turn well. Hope that makes sense 
Short List time! Thanks to your comments and suggestions I’ve narrowed it down to:
Delta 12.10
Venture Islay 12 LV
Perception Expression 14.5
Riot Enduro 13
Not to say something else won’t catch my eye, but these are the ones I’ll focus on… now keeping fingers crossed for decent road trip weather!
Valley Gemini
Length in the range that you are looking at isn’t really an issue on most rivers.
GuysNS
What you said was what I was thinking. At times it seems that someone has to be 5’3" themselves to get how uncomfortable it is to be knuckle knocking and getting a twisted up low back from trying to get a good grab in the water from the middle of a bathtub.
It looks like you have a list of boats with a leaner profle. Happy hunting!
The Islay 12LV is still over 24" wide. Both the Riot Enduro and the Delta 12.10 are 25". The Expression is a little better at 23.25".
I think you really should be looking at boats UNDER 23" if you can locate some and most of those will be around 15’ long (the Stellar 14LV is the only shorter one that comes to mind that is around 22"). There is a significant difference between these “light touring” boats in the 12’ to 14’ range and the 15’ low volume range. 15’ is not too long for winding rivers – I’ve used mine even in mild (class 1 and 2) whitewater in our narrow inland streams in Pennsylvania.
I hope you get a chance to do some on-the-water tests in various models – the difference between a 25" wide kayak and a 22" can be a revelation. You really feel like you have better control in the boat – and they are noticeably faster, especially if they are a foot or two longer. And as Celia will confirm, a slightly longer boat is easier for a shorter person to load on a vehicle because you can get better leverage.
.Another factor is hull depth – you want that to be comfortable too. I’m short-waisted, which is why I like kayaks that are more along low profile Greenland lines. My first touring kayak was 25" and that width feels like a barge to me now. The 3 kayaks I use the most are 13’5’ long by 23" (that one is a folding kayak), 15’ long by 22" and 18’ long by 21". All of them weigh under 45 pounds.
Thanks Willowleaf. I hadn’t checked the width. GuysNS, yes to what Wollowleaf said.
Guy
What’s the budget? Top end?
Hypotheticals are going to keep being suggested (as I could name a few) but what are the price parameters?
Most of your more petite paddler options are going to be longer kayaks as they shorten up more towards the Rec end of the spectrum they go wider both for Archimides and hull enforced stability rather than kayaker skill/fit keyed stability.
In the used realm I’d keep a lookout for a Necky Looksha Sport LV (Necky of old not the new Looksha), Current Deaigns Squall, Willowleaf’s fav. Venture Easky 15LV, Perception Sole, Perception Shadow, Necky Elaho DS (I know a fiberglass one around here) . Perhaps others would like to add to the potential watch list.
Any clubs or Meetup groups in your area you can post a WTB notice to?
See you on the water,
Marshall
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Once again, great feedback from everyone- much to think about!
I was thinking of the Enduro as my “max” width (25 1/4). The Delta is almost as wide, but a beautiful boat that ticks all the other boxes so I kept it on the list- for now 
Looking at the models I had crossed off the list, there are two slightly longer, narrower ones that I could reconsider, Necky Manitou 14 and Perception Carolina 14
Re budget, top end WAS $1200 cad. These models- with the exception of the Enduro- are all over budget. I am hoping (optimistically? Unrealistically?) that I can get a last season boat marked down, or that a demo/used model will be available.
PS Willowleaf, oddly enough I am Longwaisted- in a seated position hubby (5’10) and I are the same height! But I have tiny t-Rex arms
Your can find good sea kayaks for 1200 but unlike buying new it takes time and effort to constantly look nearly every day in multiple places. Good bargains are gone fast. You could get one in a day or a year it all depends on luck and effort. Something like this but a Squall https://www.ebay.com/itm/Current-Designs-Storm-GT-Kayak/183053228674?hash=item2a9ed29a82:g:Cd4AAOSwfpBadbaN