Queen mattresses are only 6" wider and 5" longer than a full bed. So, no, I don't think it would be substantially better. If you had access to one for a super good price, it would probably be worth looking into though.
I definitely think a queen would make a huge difference. I noticed the difference when my husband and I switched from a full to a queen and we didn't even have a kid in there with us at the time.
Mama to three
Mother of two spectacular girls, born mid-2010 and late 2012
We have a bed rail on one side of the bed, and that helps a lot. It is a good suggestion to consider getting one for the other side of the bed too.