Firstly, travelling abroad with a 10 month old is never going to be relaxing! Doesn't mean it can't be fun though.
I would recommend trying to find a ground floor apartment with a large terrace, or it you can stretch to it, a villa with a pool (you do need to be vigilant at keeping an eye on access to the pool though). Check out holiday lettings or owners direct.
We found self catering to be much more flexible than a hotel with tinies. They can go to bed for a nap when they want, and you can still be sitting out on the terrace, rather than holed up in a small hotel room. Same for the evenings, after the baby has gone to bed.
It's also more convenient for making baby meals, especially if there is a microwave. If you don't mind jars of baby food, just stick with those, or simple finger foods if LO is eating that sort of thing. If you prefer to make your own, take a stick blender with you.
The Balearics Islands are very nice, and generally the Spanish people love children, so they are welcome in almost all restaurants. Although maybe take one of those folding booster/high chair things, as some of the Spanish high chairs are just a tall chair that push up to the table - no straps or restraints.
Also, don't bother lugging a great pack of nappies with you, most European brands are perfectly good.