Is this banner style with email signup block possible on Squarespace?

I'm being told that the only way I can create this announcement bar with the email sign-up form is to start over again on WordPress and put my site there. I love Squarespace and can't imagine the learning curve for WordPress. My goal is eventually to turn this into a high-traffic affiliate site through advertising. I'm also told that that isn't possible on Squarespace. Can some of you experts tell me the truth and point me in a direction? Is this a job I could hire out so that nothing gets broken in the process, or is WP my best option because of SEO problems making an SP site perform well in searches? 

Thanks in advance. I'm obviously not a geek, but I love dogs and helping people keep them healthy, so I'm determined somehow to get this look (hopefully on SP!).

Thanks so much for the detailed fix!  That looks like a good option; is this something I could pay you to do?  Actually, to recreate my screenshot on the live site?  The signup in the announcement bar, the cute social media icons, the text "Helping dogs and their moms Thrive" and the navigation in the same hex code color, positioned at the bottom?

6 minutes ago, t_cross said:

That looks like a good option; is this something I could pay you to do?

Potentially, how pixel perfect are you look for compared to this mockup? Do you have a business plan or personal?

I have a business plan, I could provide the elements and hex codes, fonts Etc,