I'm busy writing a book that I've been putting off for years. In this book the main character starts off as an 18 year old but grows up to be a young adult, sometimes she will think about when she was around 6/7. My audience for this book is young adults, how should I make this book work without making young adults feel like they are reading a book intended for teenagers?
First of all you might want to familiarize yourself with book publishing marketing categories. As I explained in my comment above, the book publishing marketing category Young Adult (YA) is not written about young adult protagonists or targeted at a young adult readership, but at teenagers. It is better if you avoid the phrase "young adult" if you talk about fiction for college age readers, because that will cause confusion. Also it will help you avoid getting irrelevant search results and confusing yourself.
As for your question, adult writing isn't about the age of the characters. The Lord of the Flies is a book about middle grade kids, but it certainly isn't a Middle Grade book. What makes it or any other book adult is the narrative perspective: it is told by an adult and to adults, with the background of a life time of experiences implied in its view on things. It deals with questions that children the age of its protagonists don't commonly have.
Childrens' or YA books on the other hand usually attempt to write about the experiences of their protagonists from their age perspective. Children don't yet understand the true nature of their own problems because their ability at self-reflection and theorizing is limited. This immaturity is also reflected in the language of the writing.
To summarize, all you need to do to write an adult book is to write from your own perspective (implying that you are an adult yourself, of course), instead of trying to take on the perspective of your non-adult characters. Or, if you are older than 25 and want to write for college age kids, to not write from your older perspective but from theirs.
I've found that writing to the age group for anyone that isn't a child (under 6) is extremely limiting. I just don't do it. Instead, i separate the content types for different demographics. For example, I won't use graphic violence, sexuality, or language for a story that is geared towards young (10-17) boys.
The only changes I make to anything for younger audiences outside of plot changes are the way some things are worded and satire. That's not to say I stay away from big words...but sound too educated and some audiences will feel stupid for not understanding.
And satire only works for an audience that'll understand it. Satire is already very difficult; if you have a young audience, I recommend avoiding it altogether, as well as certain types of narrative speech like sarcasm.