Dear OP, ditch that inconsiderate person, she clearly cares only about herself, you've been with her for only UNDER a year, your dog been with you for 4 yrs. She also gets frustrated with your 'lack of progress' ? She can't wait to move ?? Wtf, you're looking to rehome your dog of 4 yrs who been with you through good and bad, to accommodate a selfish person who clearly doesn't even think about your feelings of giving up your dog, do you really want a life with someone like that ??? Seriously? She's been with you under year she knew what she's going for, she knew you've got a dog and now she's having a hissy fit because you're not getting rid of dog soon enough !!
Seriously you need to rethink your values, you sound like genuine good person whilst she sounds very self entitled selfish person who doesn't consider anyone or anything else other than herself and her new found allergies. Wonder what she will be like after marriage...
My brother in law and my sister both got kids and cats, when they got together he knew her love for pets, he knew she had one pet already, only later they found out he's very allergic, BUT, he's constantly on antihistamines, and they since got 2 more cats, it's their family, them both, 3 children and cats ...
Also, sometimes ago I was in relationship, he visited, but we didn't intend to move in together yet, I got myself a cat, I loved the cat so much, but then he decided he's allergic, sadly he made me give my cat away, I was heartbroken, he wasn't visiting very often to suffer allergy even at the start, but I cared, and I didn't have enough backbone to stand up for what right for me, So that was one of my BIGGEST mistakes, I gave my cat up, I broke my heart for person who didn't even consider my feelings, most probably cat cared about me more than that person.. Thankfully we split up few months after !
Seriously, think properly about what important to you ! And don't let someone that just entered your life to manipulate you into giving away what you care about!!!