Please tell her not to worry yet. My dd was almost completely silent (she sad mama, and nana...but they were more like mamamamamama & nananananana over and over again) until well after 2. I was SOOOOO freaked!! Autism also runs on my dh's side of the family, so I was terrified!! Her doctor told me not to worry, but I took her to a speech therapist when she was 18 months because she was TOTALLY non-verbal (wouldn't even babble in her room when the baby monitor was on...except for laughter, we never heard her voice). Dh's mom kept telling me not to worry, that both of her sons were non-verbal until after 2, but worrying is what mothers are progammed to do...so, that was impossible!!!
Sometime after her second birthday, I handed my dd a drink in a blue sippy cup, and she replied, "Mommy, could I please have the pink one?"....like she'd been talking forever.

I burst into tears, and didn't know whether to spank her, or just hug her...she could've spoken all along!! Crying, I asked her why she had never spoken before, and she said, "I didn't want to speak until I could speak like a grown up." SOOO freaky!!! Over the next few days, she began to ask me to interpret things that occurred when she was non-verbal, like "Mom, do you remember when I was about a year old, and you said to the lady with brown hair on top of her head, 'Well, didn't that just take the cake? What does take the cake mean?'" She asked me to interpret TONS of these scenarios....it was so strange!!
A few years later, at the urging of her pre-school, we took her to a psychologist to have her run thru a battery of intelligence tests. When dh and I walked into the consultation, the psychologist asked, "Has your daughter even been accused of being autistic?" I replied that she had. She said, "Well, put your mind at ease....there is absolutely NO autism in this child. She is, however, an Einstein kid." I knew very little about this, but have since learned that these are very bright children who routinely talk late (between 2 and 5). They are often non-verbal as children, and usually teach themselves to read by the time they are 1. These children sometimes exhibit similar characteristics of autistic/aspberger children, and often families with autism and/or aspberger's histories will have these children as well.
I remember the speech therapist asking me if she had her own sign language, and I replied, "No". Well, the other night, we were watching some videos of my dd as a baby, and to my surprise....she DID have her own sign language, and all throughout the videos I would "interpret" this sign language for others...it was amazing!! I had no idea she and I were playing this "game" of sorts!!
My point is....there are TONS of reasons why kids speak late. It is hard for parents to sit back and relax when other children are reaching milestones that your child is not, but it does not necessarily mean something is wrong. Please tell your cousin not to worry....I know it is hard. Get some professional advice, test his son's hearing (we had our dd's tested three times.....we were obsessive!!), and try to enjoy these years...they go by so quickly. I lost so much time just enjoying her because I was so worried that she was falling behind, when in truth, she was just developing differently.