I skipped over the other two replies so I don't know if I support them or not. This is my personal experiance:
At the time I was learning this stuff, people kept pointing to me saying "You." "You" must be what I am called if they keep insisting upon my person being called "you."
If they point to themselves and say, "I" then that must be what they are called.
I can't remember if it was my dad or someone else, but I vaguly remember someone getting really irritated. It didn't make sense because I was following along with what they were saying. If my existance was called a "you", then why were they getting so mad?
I think finally someone got it in their head to point to me and say "I" and then point to themselves and say "You".
A lightbulb went off in my head. Why didn't they just say that in the first place! It made lots more sense and I think after that I understood my name is what I call myself. Later I learned I can call myself by "I", "me" and so on.
Suggestion: Try reversing the pronoun yourself. Point to your daughtor and say "I" and point to yourself saying "You" until she catches on and calls herself "I"
We didn't start to have concerns about our daughter until she was closer to two, though looking back on things, I should have started to question things earlier. If your daughter is speaking a lot of words and knows people's names, that's a great indication that she understands language and is social and interactive. Not to say that there's nothing wrong, but I wouldn't worry too much at this point.
At my daughter's 24 month checkup, she had never spoken a single word, didn't respond to spoken language not even her name or anything, walked on her toes, flapped her arms, her eye contact was pretty poor with people other than myself and my husband, didn't understand the concept of pointing and would grab my hand and direct me around the house to indicate what she wanted, lined up all her toys, and had an obsession with stacking everything. She hit a lot of her milestones on the late side, sitting at 7 months, crawling at 12 months, walking at 16 months. We weren't concerned too much because my husband hit a lot of milestones late and didn't talk until he was 24 months old either. There's also a history of late talkers on my side of the family (my brother didnt' say a single word until 3 but then was reading at 3). The other thing was that our daughter was using our digital camera at 18 months and knew how to work the DVD and TV and was quite mechanical with everything and doing puzzles that her 3 year old cousin couldn't do, so we knew parts of her brain were developing earlier than the language and social communication side. At 24 months, we started having concerns and so did her pediatrician. Actually we had concerns at 18 months, but given the family history of delayed speech and delayed milestones, we had decided to wait 6 months more.
Anyways, I wanted to share what our daughter has, not to say that you don't have valid concerns, but that you shouldn't worry too much. Just keep questioning your daughter's pediatrician with questions you have. Ask lots of questions at the 24 month checkup. If you have concerns if her language is not what it should be at that point, if you live in the US, you can get her evaluated by the 0 to 3 federal program that provides free or low cost therapy. Many children need speech therapy but don't have autism, and they can still get speech help. Sounds like she's quite verbal. Pronouns don't usually come in until after your kid turns 2. At 24 months is when they expect kids to start combining 2 words together.
Having problems understanding the interchangability of pro-nouns is common in autism. My son did have that difficulty and couldn't understand how mum could also be called her, she, you, yours, mine, us etc etc. He tended to refer to himself by name rather than 'I' or 'me'. But this is just one aspect and there has to be difficulties in what is called 'the triad of impairments' to get a clinical diagnosis. Your daughter is quite young. It is usually from 2-3+ that parents tend to notice things are not right because prior to that age those skills are lacking in all children. As they mature they become more social, imaginative, use more language etc.
Speech and language problems/delays/or being non-verbal are seen in autism spectrum disorders. Those with Aspergers tend to have normal or advanced acquisition of language (although there can be language processing problems and literal interpretation of language).
Throwing tantrums is usually part of a toddlers development. Tantrums in autism are seen by parents as appearing out of the blue (because they don't see what has upset their child), or an emotional over reaction to what has triggered the tantrum. It also usually lasts longer and the child may appear distressed, distraught, angry to the point of getting physical etc.
Are there any other behaviours you are concerned about such as hand flapping or spinning, toe walking, sensitive to touch/pain or no apparent pain. Any problems with brushing/cutting hair,nails, teeth etc? Any tantrums around changing routines?
You can google the clinical diagnostic criteria for autism under DSM IV and I think the code number if 299.
I wouldn't be too worried at the moment. But her age is important from a developmental point of view and if you think her speech is not progressing/delayed then you need to get a speech and language assessment which may automatically mean a referral for a full assessment or you can ask for a full multi-disciplinary assessment through Health yourself.