A lot depends on budget but most modern DSLR are more than capable of taking quality pics but as just-A-snap says a quality lens will make a big difference to quality and price. For example a decent 3rd party Marco or close up lens will set you back over £300, and a decent wildlife lens up to 400mm even more. There are also some very good mirrorless systems about but I don't know much about these. I am sure you might even find a compact camera that could work and it will be better than a phone and a lot cheaper than a DSLR and a couple of lenses.
I suggest you work out a budget a take a trip to a camera shop and see what fits in her hands best, DSLR are bigger and heavier which might put her off taking it out often and that is the best way to get used to it and improve. There is also a lot between a DSLR and a compact and any decent shop will help.
I spent a almost a couple of years just using the auto mode on a basic Canon DSLR but wanted to improve so went on a £50 training course and it transformed everything and I have never used auto since and have control over my camera and the type of pictures I take.
Here is a good price comparison site http://www.camerapricebuster.co.uk/