I don't want to lie to her about my situation if that comes up somehow, that wouldn't be a good start.
She doesn't know you're married? That is something you need to disclose to her ASAP. Some women are EXTREMELY put off by going out with a married man no matter what the sitch is. I learned this pretty quickly when I started dating. It's a lot better to get that out there right away before even starting to converse with someone. If you're posting profiles on dating sites, put it right in your profile. Some women won't care but others care a LOT.
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I have accepted that my WAW thinks this is the only way she can be happy, so I'll give her the divorce she needs to be happy.
Hard to tell at this point, your sitch is still really young. You're not even 4 months into it.