I have lived in a couple of apartments in Arlington and it's going to be tough for her to find a place in a desirable neighborhood (i.e. near a metro) for 1300 a month unless she finds a roommate. As an example, I just moved out of a small 1 bed, 1 bath apartment in Shirlington which ran about 2k a month before parking and utilities which was another couple hundo. A few years ago I lived in Ballston with a roommate and we paid 2500 for a 2 bed 2 bath but prices have gone up quite a bit since then (that was around 07-08).
Alexandria can be a little less expensive, but again, anything near a metro gets a lot more pricey. I have a included a link below of an apartment complex right near my house. It appears to be in her price range and the apartments look ok. Not great but pretty good. We are about 2 miles from a metro but there is bus access. I have met many people that live in these apartments and they all seem happy. I have not seen the inside though so that may be a factor.
http://www.foxchaseofalexandriaapts....1002,1006,1007
I am not sure what her vehicle situation is like or where she will be working but if she is willing to commute, there are loads or places to live within 30-40 miles of DC that offer A LOT more for the money...she just will have to commute.
Hope this helps. Let me know if you have any questions.