What netbook do you have in mind? What are it's specifications? Also, what type of office work would you do on it? Simple documents and spreadsheets, or enormous spreadsheets?
If you're content doing your work on a three year-old laptop, a new netbook would likely be fast enough for your needs.
If possible, go to a store that has the model you'd like on demo and open up MS Office and play around, see how quickly it responds, how comfortable you are with the screen size/keyboard size, etc...
Your boss might be dismissing it because of something he's heard from someone dissatisfied. It will be a lot easier to convince him if you can tell him you've played around with the one you'd like.
Also, look at reviews online for the model you're considering, they often have benchmarks that will help you gauge the general performance compared to other models.