Well, I'm not sure exactly what you're doing now (or even why 7 taps is necessarily a large number) ... and I think it depends a little bit on exactly what browser you're using.
But typically there's a "share" option in the menu, so in the basic Android browser it would be Menu->Share->Gmail->start typing name->select name->Send. So, that's 6+ taps (depending on how many letters you have to type to find your name). Seems pretty reasonable to me.
There's also the question of why you're trying to email a link to yourself. If you use Chrome you can just have shared bookmarks, which may be a little easier.