I was worried about my first son, too. He didn't really know that many words, I thought. We could all tell that he was a very smart baby, but at his 18 month-old check up, I was concerned enough to bring it up to the doctor. He took me seriously and told me what to do.
He told me to go home and write down all the words he said during a day. He said that I would probably find that he knew more words than I thought he did. He also said that animal sounds count. That put my mind at ease, because my son could do a ton of those. So that bumped up his word count significantly.
And he also said that our use of sign language didn't really delay language development. In fact, it speeds it, but in a different way. Signing kids learn language patterns and structure earlier than other kids, and they usually learn a sign and then learn the word shortly after. But since they can speak with their hands, if they're uncomfortable making a certain sound, they'll just sign instead (for example, my 2nd son couldn't say "orange" until he was well on his way to 3 years, so we thought he didn't know that color. Turns out he did, we just had to ask the question in a different way so he didn't have to SAY the word orange. With my first, I thought he was red/green colorblind because he called both colors "green." Turns out he had a hard time saying RED, so he just substituted.)
He also gave me a "game" to play with my son, to test his verbal learning capacity. As I was handing my son something, such as juice, for example, I was to not give it to him right away, but hold it just out of reach and say, "Juice. Juice." If he began to show even a tiny sign of frustration, I was to just give it to him. And I wasn't to do it with every single little thing, just easy-to-say words, and just several times a day. The doctor said I should be able to see my son pick up a new word or two soon, within a day or two. If he didn't, he said they'd do some testing at 24 months.
Thankfully, my son learned a new word the first day. I knew he was capable of learning new words, so I stopped worrying. Hopefully your daughter will "play along" and ease your mind.
Oh, and about others not understanding, that's fine. I don't have the stats on how many words others should understand by what age, but I'm sure you can google that. I still have to translate sometimes for my 4 year old, and he's more than fine.