For some strange reason in my experience, Dell underrates their power supplies.
If you have a standard dual core processor that is not a super high clock (being a Vostro I would assume something like a Pentium Dual-Core E2180) and a single hard drive and optical drive with few peripheral devices, you may have the headroom to run that card.
If not, I would look into buying a 350 watt FSP power supply which is underrated, inexpensive and of good quality. You can try it, and if you get stability issues, immediately upgrade the power supply.