I had severe morning sickness with my last pregnancy and was underweight. I had lost about 8lbs but my dr didn't seem concerned and said it was normal in 1st tri. I asked for Zofran for my benefit only and he obliged.
My point is that I was underweight and lost more and the dr still wasn't concerned. It seems pretty drastic to me to get an IV of Zofran. I would absolutely ask the dr if they felt this is completely necessary. I should also add I went on to gain 56 lbs that pregnancy so all turned out fine. :)