i know i'll probably get shouted at for this but nevermind. should you give that to your new gf? hell no. you're right, it is cheesy, and it is crap.
i'm not about to go into the literary value of the poem (none) since that is clearly not the point of your endeavour. nevertheless, i implore you not to let her see that, if only because it may really freak her out. i know very few girls who would appreciate getting that off a new boyfriend... it's just cringeworthily keen. if you'd been together for years and years and you could be sure that something like that wouldn't shock her, i'd say go for it. the sentiments are sweet and all, but the expression is so cliche and the timing so poor that if you give that to her, the chances are that she'll either a) laugh, or b) say "aww that's really sweet." and laugh when you've gone. with her friends.
i'm sorry if that sounds harsh, but i think honesty is the best policy here. just don't do it. or, as someone else said, steal an actual poem and give her that.
edit: if you're 14 or under, the poem is fine and is just one of those life mistakes that you have to make.