YANBU - the dog will never let you down. He already has by suggesting that you part with a family member, albeit a canine one, that you love and and has shared your bad times, and has, as you admit, got you through them.
He may be a lovely bloke in other respects, but he obviously has no idea (or doesn't care!) how much this will distress you - and how much it will affect your relationship, because it will.
I suspect MrsTerry is right, and that he would expect you to murder (not too strong a word IMO) your lovely dog if she couldn't be re-homed (and it ishrdto re-home an elderly dog, and also not at all fair on her. She won't know why she is suddenly unwanted, even if she goes to lovely people.
Also, if she is re-homed to (say) your aunt, there is always the chance that you will find life without her unbearable, and will want her back - and he won't like that.
I'm allergic to cats. The allergy didn't manifest until ours were well adult (that's the thing with allergies - sometimes they just "happen"). but there's no way I would dream getting rid. I just sniff my way through life with lungs lined with cat hair.
If you part with your dog, you will always regret it and the guilt will haunt you. (I speak as someone who has had to have animals PTS for medical reasons. It is never easy.)
If he is "the one", he will be prepared to continue as you are for as long as it takes, or put up with any sniffling and sneezing.
And in future, you can stick to poodles or bedlington terriers.