[gunnr]

No worries, you’re on the right path.
Get the obedience locked down. Assume nothing, and start from ground zero.
Two devices from the hunt community will be of great value to you.
Get some type of a location collar on her. A bell, electronic tone, etc. When you are finally able to turn her loose, you can keep track of her audibly. You be stunned at how fast they disappear into the background. You may not see her, but you can hear her.
If you have no aversion to using an eCollar, I highly recommend one. They’re not a shortcut, but they will condense the time for you. Some models can perform the role of obedience, location, and point. ( If she goes on point naturally on her own, she will be dead still, and make no noise. You need to be attuned to this, to avoid correcting her, incorrectly.)
If you can get her out, and off leash, as often as you indicate, she will take care of the mental stimulation herself.
You don’t need much space to train the obedience component.

 

[gunnr]

If you’ve not used a “ check cord” previously, it is insensible for getting your girl off on her own in the brush,
Buy 50’ of soft cotton rope, make a loop in one end for a snap to put on her collar, but preferably a full body harness. Leave the other end bitter, no knot.
When she starts moving about, that 50’ of rope gets tangled in brush, and kind of “ ground ties her in place” until you free her.
The reason for not putting a knot in the bitter end, is that you want the rope to act like a progressive brake, and slow her down to the stop. A knot can get caught and bring her to a very abrupt stop. You don’t want that.
Have fun with her.

 

[gunnr]

I would say that for the first few weeks, coddle her a little bit more than you might normally. The time for some tough love will come, but you really need to know her better.
Her whole world has been turned upside down, and despite what many believe, I personally think that dogs know it is, or has, happened, and it stresses them out to no end at times. Be gentle with her for a few weeks.
The in your pocket, constantly wanting to be by your side, behavior is kind of a breed attribute, so is the whining when she doesn't get to accompany you. My dog, Finn, is three years old, and I can't get in and out the back door without him wanting to "butt in". Finn suffers from zero separation anxiety.
"Generally", true separation anxiety is accompanied by other negative behaviors like tearing things up, trashing their kennel/crate, urination, uncontrollable barking. The dogs also start to really get their heart rates up and pant/slobber like you wouldn't believe. If she's just kind of whining a bit, let her go on some trips to empty the trash, and make her stay for some trips. She needs to establish with confidence, the pattern in her mind, that when you go out the door, you will be coming back.

Even though she has her full adult size at this time, she is still very much a puppy, and will do puppy behaviors. You have to look at her like a puppy, and make no assumptions based on her size. The more consistent, and regular your routine, and the more predictable your behaviors are to her, the quicker she will settle down. Animals thrive on a regular routine. It brings their stress levels way down, when they can pattern associate what is going to happen next.

I think in a few weeks you're going to be fine and having a riot of a time with her.

Oh, one more thing. There really is no limit to the length of a check cord. 50' is just a nice length. I've had mine on 100-150 yards of parachute cord, in big open fields. My dogs are meant to hunt, so I like to get them out and away from me as early in life as possible. As adults, when I cut my dogs loose, they'll typically be within a 50-100 yard radius of me. I don't want them to remain close to me, unless they need to be. That's why I use such long cords.

 

[gunnr]

Praise, Praise, and more Praise!!! You are a very lucky person. This can be a key behavior to accelerate your training. Let her bring this out to maximum development.
Look up internet articles on staunching a dog at point, and steadying to wing. A dog that does it all on it's own, with no breaking, is very much desirable.
Squirrels and Vizslas are "just a thing". If you don't want her to mess about them, you'll need to train in the "leave it" command. Squirrels are easier than rabbits though. they just run for the nearest tree, and you can get your dog back easily. Rabbits take off and you have track meet on your hands. I am so glad Finn has zero interest in Rabbits! I haven't always been that fortunate.