Our house is half tile and half carpet, so I know your fear! I kept him in the carpeted areas as often as I could. His play area has the foam mats and I love them! You will find that things get scarier when she is 2 and loves to jump and spin all the time! They are very resiliant! We have had a couple of falls and some nasty bruises, but he has always been fine. We went to the ER once for a nasty fall to the check. The ER doctor said that if they do not loose consciousness or act funny after a fall, you can just give tylenol and ice (if they allow it!).
In you situation, I would focus on the couch and bed areas. Maybe have a thick area rug next to those areas? This are prime areas for climbing and exploring in the next year! She will fall eventually, but if you are there watching, she will be fine. It is amazing what their heads can withstand!!
On the plus side, I would LOVE to have tile in my dinning room, you are lucky!