On her birthday, spend some personal time with her and get to know her. Avoid talking about the relationship; if she mentions it just say: "I'm sorry" and take note of how often she says it.
More often-than-not women will cling to their ex; the last thing you want to do, is to approach her when she still cares about someone else. If you approach incorrectly, she has all the more reason to shut you down; and if you approach correctly/start dating her and she eventually finds out you're not the same man as the one she loves, well... You're out the door.
So what I'm saying is that you should be calm and contained. You don't just scarf down dinner, you savor the taste while you relax. You want to enjoy her company, not just jump into it at full speed. Learn her likes, dislikes, what she does for fun, her bad habbits, etc..
>> Key Point:: Get to know her. Keep the spotlight on her and feel free to share what you are like in small increments.
Definitely go for it! What's the worst thing that can happen? Plus intuition is really strong and if you have a gut feeling, go with it. Start off slow since she did just get out of a relationship, just a casual conversation, go for coffee, nothing that shows commitment. But things will get interesting if you two do have chemistry...
honestly for now I would take the whole thing slow and not aim for a relationship at this immediate time . now I'm not saying you can't try for a date with her just don't feel it has to be a serious relationship rate away .
for the mean time try talking to her when you can , so you can get a better feel for her level of interest in you and if she seems interested ask her out on a not so serious date
It's been a long term feeling so it's not just one of those hey she's hot quick interests. I would go for it. Hang out at church then ask if she would like to go out for lunch. (still as friends) then after lunch as your saying goodbye if everything went well and your feeling it and you can tell she feels you then ask her out to dinner during the week. It'll make her day
Seeing her at church and wishing her a happy birthday should be nice. She may not be ready for a relationship if she was dating this other guy for a year, so just take it slow with her, you don't want to just end up being a rebound guy. I really don't know what to say in terms of how slow because if you take it too slow you're just going to get friend zoned, you may already be, just try to spend more time with her and find out if she does still have feelings for you, you should be able to tell this within a month.