At 11 weeks of age, you cannot expect your puppy to hold her pee/poo for more than 3 hours at a time. The general rule for puppies is age in months +1. For your pup, 11 weeks = almost 2 months +1 = 3 hours MAX. Puppies are still developing sphincter and bladder control, so this is the maximum time they can hold it, not the number of hours they *will* hold it. So take your pup out every 2-3 hours or more often if necessary. As she grows older, the time you can leave her alone will increase.
Take your dog out on a leash each and every time she needs to potty. Go to the same spot every time, and give her the potty command. Don't let her play and get distracted. She needs to associate the command with her going potty. When she does poo or pee, praise her like she laid a golden egg and give her treats. Only after she eliminates should you reward her with a walk or play time. If she doesn't go within 5 minutes, then take her back inside but confine her (a crate or bathroom or pen). After 20 min, repeat the process of going outside.
If she every pees/poos inside, don't scold or punish her. Just clean it up with an exzymatic pet odor/stain remover like Nature's Miracle. It's your fault for not taking her out sooner. At the same time, you're not rewarding her with treats and praise, so you're not providing any incentive for her go inside.
Expect puppies to have to eliminate after waking up from any sleep/nap, after every meal, after any rigorous play, and generally whenever you switch activities. It's a lot at first, but consistency and patience will pay off.
Also, your puppy does not need full run of the home unsupervisded until potty trained and housebroken. When you can't supervise her, either put her in the crate or get an exercise pen on top of vinyl sheets to place in your bedroom. Remember you still have to take her out ever couple of hours.
A few words on CRATE TRAINING:
Crate training is not cruel if you use it properly, and can be a valuable training aid as well as a safety den for your pup. A puppy should not be crated for longer than 4 hours at a time. That's a long time for a pup. For an adult dog, I believe it's no longer than 6-8 hours.
If you choose to use a crate, here's how to get your dog accustomed to it. There are a few cardinal rules:
1) Don't leave a dog confined for too long.
2) Ignore all whining/barking.
If you give in, the dog will learn that barking/whining=attention and getting her way and you will have created a monster. Completely ignore the dog, meaning no eye contact, no talking to the dog (no poor babys, no shut ups), absolutely no attention whatsoever. This may take a week for her to catch on. My pup started out barking/whining for 40min straight before falling asleep. I just tuned it out completely. By the end of the week, she would bark for a couple minutes and then be fast asleep. Now she doesn't fuss anymore at all.
3) Only let the dog out of the crate when she is calm and quiet.
Be consistent, and she will learn that the sooner she behaves properly (calm and quiet, not barking/yappy), she'll be let out. My pup will now bark/whine when she needs to be let out to go potty in the middle of the night, but otherwise, she stays quiet. She knows whining/barking won't help her get her way.
4) Always be matter of fact when putting dog in the crate.
Don't coddle, don't baby, don't be angry. Just pick up the pup and place her in there. Give her a treat and a favorite safe toy though.
5) Never use the crate for punishment. Keep it a happy place.
Don't use excessive force to put the pup in there. Don't show any anger when sending your pup to her crate. If she's being rowdy and needs a time out, then pick up the pup, say in a sing-song voice "you get the crate prize!" and plop her in there. You want the pup to associate the crate with good things so that she'll learn to seek it out and use it as her den.
6) Never make a big deal of getting out of the crate.
In fact, just open the door and walk away and ignore the dog for a couple min when released. You don't want her to think that getting out of the crate is such a huge reward, because that only makes being in the crate a negative thing. After a couple min, give her attention and praise.
HOW TO:
During the day, place your pup in there for short periods of time (~5 min). Give her a treat and a favorite safe toy. If she's quiet at the end of the time, open the door and let her out. If she's whining/barking, leave her in there until she is calm and quiet. Once she's stopped barking (even for a few seconds), let her out. Repeat this several times throughout the day, every day and slowly increase the duration that she is left in there.
CRATING BENEFITS:
Crate training will help with house breaking because you have a safe place to put your pup when you can't supervise her (while sleeping, cooking, taking a shower, running an errand, etc) and she can't hurt herself or destry anything while crated.
It will also help with potty training because dogs naturally do not want to soil their sleeping quarters. Your pup will try to hold it in as long as she can while in the crate. If she soiled the crate, then you left her in there too long or the crate may be too big (if she can pee/poo in a corner and sleep in the other end).
If ever your pup needs to be boarded or kenneled, she is already familiar with being in a crate-like environment.
If she ever is injured and needs to be confined and her mobility restricted, she will already be comfortable with staying in a crate.
If traveling in a car, it's safer for the pet to travel in a crate. In case of an accident, you're pet won't be tossed around if in the crate, and is less likely to be running loose in traffic.