It is perfectly fine to record with the speaker if she sings better that way. The only problem would be spillage of the music from the speakers into the vocal track. Dont have the speaker too loud to reduce spill. If you want to try to eradicate as much spill as possible from the vocal track, here is a neat trick:
Record the vocal track like normal, with the music playing out the speakers. On this track you have both vocal and spill
Record a second time, but this time without the vocal (i.e. just record the music from the speakers, using the mic - which you have left untouched along with all volume settings!). This is the 'spill' track.
Now, invert the phase of the spill track and play it along with the vocal track. A lot of the spill should be eradicated now
Also, when you setup the mic and the speakers, try to use a cardiod or hyper-cardiod mic and have the null point of the mic pointed toward the speaker, thus reducing the amount of speaker sound that the mic picks up.
Well made headphones with very little sound leakage are of course a preferred method as chris says, as they allow you to record a perfectly clean track, no spill. What you can do to make it easier for the singer, is put a bit of processing on the output channel of the DAW to allow her to hear herself better and to 'flatter' the voice a little. Some compression so that when she sings loud it doesnt bust her ear or when she goes very quiet she can still hear herself, and a little eq to cut out all the rumble below 100hz and maybe a little lift in the 5khz region to help her voice cut through and be clearly heard.