First, we need to convert the length of the rolls of ribbon from feet to inches.
There are 12 inches in a foot, so a 9-foot roll of ribbon is:
\[ 9 \text{ feet} \times 12 \text{ inches/foot} = 108 \text{ inches} \]
Now, since there are 15 rolls of ribbon, the total length of ribbon that the dressmaker has is:
\[ 15 \text{ rolls} \times 108 \text{ inches/roll} = 1620 \text{ inches} \]
Therefore, the dressmaker has a total of 1620 inches of ribbon.