Is she too attached?

My little girl (2y/o) seems to be very attached to me, but I'm scared its unhealthy for her. I unfortunately wasn't able to get a second rat, so she is by herself. I often have her with me so she doesn't get lonely. The thing is, when I set her down she doesn't like leaving my lap. She may venture a little bit, but she comes back to me. When I get up, she goes to the edge of the couch and will wait for me, and sometime she even cries. When I bring her to the park, she won't go farther than 2 feet from me. Is this amount of attachment normal or unhealthy? Is she just shy?

Considering the facts that she is a senior rat and has no rat companion, it's not surprising that she wants to be close to you. Plenty of rats at that age would prefer to just rest and cuddle and may not be as hyper/playful. Rats need companions and company, and since she doesn't have a rat friend you have to cover the comfort that she would get from having a friend with her 24/7.
It's not surprising she is so attached to you, considering she's alone.
What do you mean the park?

What worries me is the crying as rats are not usually vocal

The whining is a concern. I'd get her vet checked.
How very unfortunate for that little girl to have to live alone, without a buddy.

Yeah I've definitely learned with her that she needs buddy. Luckily, she gets attention 90% of the time that she is not asleep. And I mean park as in I'll occasionally take her to our local park and let her hop around the grass (she loves it!) to get her energy out and have her get a little more nature time since her cage isn't the most open space. She has a rat friend that she occasionally visits so she doesn't get too lonely. The crying is what concerns me too.

Can you get a video of her crying? I've never heard of a rat doing that before.

Also, at the park, be wary of predators. Birds can swoop down and grab rats in a quick motion. I think it would be beneficial to get a large rabbit cage and remove the bottom tub, then place that over her so she can feel the grass but is still enclosed. I believe you that she won't run away, but it's those odd-ball scenarios where you just want to be safe.

Also, I recommend getting a pair of two adult females (same age) to keep her company. Babies would be too much for her, I'd think. When your girl passes, the other two females will have each other. I find that it's never too late to introduce rats to friends - they have some socializing instincts that never go away. Just be sure to follow proper introduction steps and do not rush it!

I totally agree with being careful about predators. Fumblesquid's idea of putting a cage/enclosure on top of where she's in the grass is a great suggestion. I would also worry about pesticides in the grass.

I'm wondering if what you're perceiving to be "whining" is actually respiratory disease? As others have mentioned above, rats don't normally vocalize. She could be getting stressed when you leave her and the sound you're hearing is a wheezing sound.

Great idea to see if you can get her some friends, too. I know it's not easy thinking about introductions and adding more rats, but it could help her feel more comfortable and less lonely.