What's the protocol on stealing from other poets?

I was just wondering what the protocol is on borrowing another poet's line as the jumping-off point for your poem, or writing a response to their poem. Is it still publishable? Or is it just a lame writing exercise?

Because I have two poems I've written I don't know what to do with. One was written in response to Robert Frost's "Love and a Question", and one was written with a first line of Emily Dickinson's, "Bring me the sunrise in a cup..."

And if I can't do anything with them, I want to know why I wasted my time. :p I've never been a fan of the "imitation" school of writing that various teachers and professors have had me practice over the years.

Here's "Love and an Answer", my response to Robert Frost's. In his poem, written from the man's perspective, he is keeping some secret from his loving wife in an attempt to protect her.

Love and An Answer

Inspired by Robert Frost’s Poem
Love and A Question

She sat by the firelight, bending over her little work
And her needle went steadily, as he paced by the door.
She sat before the open fire, dreaming happily of him
And her skin flushed pink before the reflected heat.

She looked up often, and he would smile back
But his eyes were worried, and she bit her lip to think.
So she laid her work by her side, and went to him
As he stared out on the darkened road.

She took his big hand in her two and asked to know
And he just shook his head, wishing to keep
Her heart ever as happy and bright as it were then
Her face ruddy from the fire, her lips warm to touch.

And then darkness fell a little, into those pretty eyes
To think that there were secrets he would keep
And thought he wanted only to bear this burden
Even without knowing it had become her own.

He felt the rift, that separating his pain from her’s
Was to deeply separate himself from her,
And so he told her, with a shiver from the open door
And she pressed her warm body against his.