About 3 weeks ago we took her to the doctor for her MMR vaccination and since then we noticed that she gradually lost her appetite and refused to eat.
The timing of this change in appetite is obviously somewhat alarming to you. Parents often have a pretty good sense of if their children are truly ill (or different.)
You've seen two doctors now who have tried to reassure you, but you are still concerned. It's time to start collecting evidence, for your sake (and ultimately for the baby's sake.)
Stephanie gave good advice about dehydration. When it's that obvious to you, it will also be obvious to the doctor, so how do you judge less eating and drinking that doesn't produce such clear clinical signs?
Weigh her diapers.
Get a scale that measures grams. Weigh the diaper before you put it on; then weigh the diaper within a couple of minutes of coming off (or curl it into a ball so it can't dry out, and weigh as soon as possible.) That's called urinary output. Write it down every time. Record the poop and it's consistency, too. If she's only mildly dehydrated, her poop will be drier/harder, because the colon reabsorbs water from fecal matter. The less hydrated she is, the more water is reabsorbed, and the drier the poop will be.
Try to record her fluid intake, too.
This will be harder, because of spillage, guestimating, etc. Together, this is called I&Os - intake and output. If you're breastfeeding, this will obviously be impossible.
Don't bother recording her food intake.
If she is truly eating less over a sustained period of time, she will fall off her growth chart. At 14 months, she won't take long to do this. This is a girl's growth chart. It's used pretty much all over the world. You can get her previous readings from an office nurse (get the dates, too) and plot them out yourself.
Take videos of her playing and interacting.
Compare them to videos taken before. Are they really different? How? Make notations of loss of skills.
Doctors are human. If you're worried that this is vaccine-related, they will try to reassure you that it's not (and with good reason), because vaccine related illness is very rare. But not even doctors can argue with well-documented facts.
Do I think she's suffering from a vaccine-related illness? No, I don't. However, though rare, it's not impossible. Also, as stated by others, this could be any number of things, most of which are not serious.
I believe that in the presence of food and water in plenty, a normal child will not starve or dehydrate. You've seen two doctors who found nothing remarkable. Give it some time. It's not as if an anti-vaccine shot exists that must be given as soon as possible to make a non-specific cluster of symptoms disappear.
If she's becoming more constipated (stools are drier/harder), falling off her growth chart, or is, in a way that can be documented, different from before, take her back to the doctor with facts in hand. Facts are harder to ignore, and a reasonable doctor will look at them objectively. If the facts document that something has changed and the doctor still doesn't pay attention, ask for a second opinion.
My guess is that she will be fine, and this is the best anyone can do over the internet: guess. You, however, can do better. You can gather facts.
I hope this helps you to feel less powerless in this situation.