I don't think so. Even dSLRs don't record 1080p at 60fps.
Say what? Yes they do; there's plenty that do.
High speed movie
You can't sort by 1080p60, but looking through that filtered list you can find a lot. Here's a few examples:
http://www.dpreview.com/products/sony/slrs/sony_slta99
Resolutions 1920 x 1080 (60, 24 fps), 1440 x 1080 (30fps), 640 x 424 (29.97 fps)
http://www.dpreview.com/products/panasonic/slrs/panasonic_dmcg5
Resolutions 1920 x 1080 (60, 50, 30, 25fps) 1280 x 720 (60, 50, 30, 25fps), 640 x 480 (30, 25fps
Videography notes 1920 x 1080, 60p, 50p (sensor output is 60p, 50p) (PSH: 28Mbps) ; 1920 × 1080, 60i,50i (sensor output is 60p, 50p) (FSH: 17Mbps) ; 1920 x 1080, 30p,25p (sensor output is 60p, 25p) (FPH: 17Mbps) ; 1280 x 720, 60p, 50p (sensor output is 60p, 25p) (SH: 17Mbps)
http://www.dpreview.com/products/sony/slrs/sony_slta37
Resolutions 1920 x 1080 (60, 29.97 fps), 1440 x 1080 (30fps), 640 x 424 (29.97 fps)