Queen size is usually around 84 X 92
Without a picture of the quilt, can't determine if it's a quilt that can be easily disassembled and reconstructed differently to make a larger size, or one where you could simply add more blocks.
Without knowing that I can only comment on enlarging by using borders. Modifying yours by using borders would require very large borders indeed (24 on one side, 22 on the other). I dont' have a queen bed to measure, but if the size of the quilt you have now centers/covers the top of the bed edge to edge, it may not look bad/odd by adding really wide borders for the overhang.
If you would like more suggestions, it would be best to add a photo so we know how to best achieve it.
If you plan on continuing with quilting as a hobby though, go ahead and bind the one you have and plan a proper Queen size that you would be happier with. If quilting does indeed agree with you, this won't be your last quilt :)