Yes, that PSU does seem a bit on the soft side. It may indeed supply enough power to the thing when it's running MS Word or whatever, but the moment you start adding bits and peripherals to your computer, and then taxing the PSU with a 3D application, it could become a weak link in the chain. So it is perfectly possible for the thing to just say 'sod this', and check out on you (either temporarily, or permanently, sometimes you smell burning, sometimes not). I've had both versions of that scenario, and it took me a while to figure it was that when I was having the old blue screen of death. Now I always use heavy duty PSUs, as they have plenty of leeway for adding other bits and pieces, such as network cards and the like without leaving the GPU short on juice.
If you do uprate the PSU (which is easy to do by the way, it's just a few posi screws and a bit of reconnecting wires, but taking a photo of where things go before you disconnect stuff to assist you, is a good idea. Unplug it from the mains too, unless you want to die. Also make sure you have one that has the same plug for the motherboard as your old type, there is more than one sort, so take your old PSU out and compare the main plug on it to the one you are considering buying), then be aware that you may need to add another fan to the case somewhere to assist cooling, there are usually extra unused vent locations on a PC case for this purpose (sometimes you have to remove metal panels that have weakened 'break lines' on them to clear the holes for the vent) and there are also usually a number of pins on the motherboard which you can take power for the fans from, if you haven't got a manual for your motherboard (not unlikely if it is a Dell), do a search on the net for a diagram of your motherboard and it will mark locations or power points for fans. If you need to know what type of motherboard it is, do a search on the net for a little utility called CPU-Z (shareware, or free if you are too cheap to donate LOL), this analyses your system and tells you the spec of all your stuff in your PC.
Chock