My son was the same way - he said absolutely nothing, but he grunted/whined and pointed at what he wanted. The doctor wasn't really concerned because he wasn't delayed in any other area, and he could hear just fine. Finally one day I just got sick of it - he was in his high chair, grunting and pointing at the cabinet. I said, "Look, I don't know what you want. Whatever it is that you want, just say the word, and you can have it. But you have to stop this whining!" I just said it for myself, you know, to vent frustration. But that kid looked right at me and said, clear as day, "COOKIE!" I guess I should have been thrilled that he said his first word, but my reaction was, "You little stinker! You could talk all along!" After that, he never shut up.
I'm not saying that what I said worked. I wish I had been more supportive and just coaxed him - but truthfully, I had done that for months. I think it's possible that my true inability to figure out what he wanted might have had something to do with it, or his shock at my tone of frustration maybe prompted it. I did have a gut feeling, an instinct, that he might respond to me without being crushed at my tone, I will say that. He had a very strong personality and I didn't feel he was emotionally fragile in any way. Or, maybe he was just ready. I don't know!
All I can say is, if your daughter is not delayed in other ways, don't worry. It will happen. I don't know if your older daughter "translates" for her, but it might help if she didn't. Perhaps if she pats her head, you can say "Do you want a hat?" and after that act like you don't know what she wants and ask her to say the word. Don't push (like I did!) if you aren't comfortable or don't feel it's right for the situation or her personality.
You can consider some evaluation if you feel it's best. If you don't like your doctor's response, you can get a 2nd opinion. I do wonder if teaching her sign language at this point is going to get in the way of her verbal development though. She is physically and cognitively capable of speaking - I think sign language is more for younger children who are not. But as always, it's your decision. Good luck!