Can you stretch your budget to about $400? Many options open up when you get to that point.
DSLRs range in price from around $400 up to about $6000 or more. The entry range cameras are typically all under $1000 for both the camera body and at least one starter lens (often referred to as the "kit" lens because it comes with the initial package.)
However, even in this sub-$1000 range, there's a subrange of the entry-level bodies and they're typically around $500 or less.
On the Nikon side you'd recognize them because they have the letter "D" followed by a 4 digit number that starts with a "3". E.g. "D3000", "D3100" are very old, but you can still find the "D3200", "D3300", and "D3400". The "D3400" is what you can think of as "this year's model". Nikon also has a D5000 series (D5100, D5200, etc. etc.) and those are still in the entry range, but higher in the entry range. Of course Nikon also has mid-tier and pro-tier bodies as well.
On the Canon side, you'd recognize the cameras because they all have "Rebel" in the name and the models are all "T" followed by a single digit number. So there's the T3, T5, and T6 (there was no "T4" - they skipped that one.) Similar to Nikon, the higher the number simply means it's a more recent model. So the "T6" is "this year's model" and the T5 was "last year's model", etc.) Like Nikon, Canon also offers a series which is still entry range, but in the higher end of the entry range, and you'll recognize those because they put an "i" suffix on the model. E.g. "T6i" instead of "T6" (and people sometimes get confused to think that the T6 and T6i are basically the same camera with some minor feature differences... they are not. They are completely different models. And of course there are also mid-tier and pro models as well.
We are just about to the time of year when Canon typically announces "next years" new entry-level camera. If they stick with their naming convention then they'll introduce a "T7i" and maybe a "T7".
BOTH Nikon and Canon have a "refurbished" section to their own online web store (so you buy the camera direct from them rather than a typical retailer). These are cameras that cannot be sold as "new" but they've been refurbished and come with the very same "new product warranty" (for Canon it's a 1 year warranty, I am not sure if Nikon's is also a year but they tend to just match each other so I expect it probably is 1 year) that a new (non-refurbished) camera would have. ... but the price is a lot less.
And while you do save by purchasing the "refurbished" version of "this years model" ... you save even more if you buy the "refurbished" version of "last years model"... or even the year before that. But at least you're getting something that is factory refurbished (so it'll like like it's brand new) and it comes with a factory warranty. This is a lot nicer and less risky than shopping for used gear where you have no idea how it's been treated and how well it works. It's one thing when an experienced photographer shops for used gear... they actually know what to look for and how to tell what sort of shape the camera is in. But since this would be a first-time purchase for you, you'd have no good way of knowing if a used camera had some significant issue until it's too late.
Often a refurbished camera never had anything wrong with it... someone bought it and changed their mind and now it can't be sold as "new".
It is generally possible to get a refurbished camera+lens combination for less than $400.
A refurbished Nikon D3200 (with kit lens) is about $350 from the Nikon store.
A refurbished Canon EOS Rebel T5 (with kit lens) is $279 from the Canon store.
See:
Canon Refurbished EOS Digital SLR Cameras | Canon Online Store
And:
Refurbished Camera Products | Used Cameras, Lenses & Flashes | Nikon
The camera will not magically increase her photographic expertise. It's a tool... sort of like buying a nice musical instrument... it only works if you learn to play it. These cameras can do far more than a smart-phone camera... but getting those results requires some learning. Some specific types of results require some extra gear (different types of lenses, lighting, etc.) but this is the foundation.
I typically suggest adding in a good book... such as "Understanding Exposure" by Bryan Peterson or the entry book to Scott Kelby's "Digital Photography" series (which is a series of several books). They give you the grounding of how to exploit the camera's capabilities to get more creative shots by understanding how settings alter the results you'll get.