Please check the protocol by Dal Grande et al. (free available) for algal cultures.
http://bio-protocol.org/e154
My experience with the Qiagen DNeasy Plant Kit is that it works fast but - depending on the algal species (more or less polysaccharides, phenols etc.) - DNA may still contain too much PCR inhibitors. Therefore, if you use this kit, prepare dilutions of DNA to reduce the proportion of inhibitors before you perform a PCR.
Alternatively, you can extract DNA with the MoBio PowerPlant DNA isolation kit that wash inhibitors very well. MoBIo was taken over by Qiagen recently.