|Very common evolution diagram. Image Link|
It is important to note that the gap in the fossil record is closing with new studies and new fossil evidence. Transitional fossils are in fact not rare. Here's a link to a great website discussing what we know about transitional fossils.
If you haven't, read the book "Your Inner Fish" by Neil Shubin, an evolutionary biologist. You can also find more information, including options to watch the "Your Inner Fish" documentary, here:
I watched this documentary with my 10 year old a couple of years ago and it was fantastic! One of the episodes focuses on transitional fossils and explains they are quite common. Yes, there are still gaps in the fossil records, but those gaps are quickly closing as more studies are done and more evidence is discovered.
To conclude, no, the gap in the fossil records does NOT disprove evolution.