The Mexico striker scored twice in United's 4-0 midweek win over Norwich City in the League Cup and has consequently given Moyes a selection headache for this weekend's match at Craven Cottage.
Hernandez has frequently been used as an substitute behind leading strikers Robin van Persie and Wayne Rooney this season, but Moyes praised the attitude shown by the 25-year-old and said Hernandez, far from being content with his bench role, was among a number of fringe players at Old Trafford pushing for regular first-team football.
"I've been really pleased for Javier because it's been a slow start for him," Moyes said on Friday. "It's been a difficult summer coming back and then back and forth to Mexico for all the games they've had to play.
"But he's started to do what he's done over the years which is to score goals. He scored in midweek so long may that continue. I think, like everyone, he's desperate to get into the Manchester United first team and we can see that every day in training.
"The players have got a brilliant attitude and are always trying to impress every day and we've already introduced one or two young players into the first team. And if any more of them do well we'll continue to put them in.
"We've got a big squad, they're all first-team players and in their own right they could all be playing every week, so we'll continue to try and use them at the right time and bring them out when we see fit."
United gaining momentum
Meanwhile Moyes, who succeeded Alex Ferguson in the United hotseat in the summer, said the club's recent form suggested they were on their way to climbing up from their unusually low current position of eighth in the table, eight points behind leaders Arsenal.
"We've started to pull together one or two half-decent results, and hopefully that starts to build a bit of momentum," Moyes explained.
"We have been a little bit up and down at the start of the season winning one and losing one, so we're hoping to try and get into a bit more consistency and it will follow with that."
Moyes confirmed van Persie has shown no ill effects following a recent toe injury which has seen him rested for certain matches.
"He's been fine, he's been training well," the Scot said. "Robin's worked quite well this week so hopefully he'll be OK."
And Moyes said both centre-backs could be involved at Craven Cottage, although striker Danny Welbeck has been ruled out of the trip to London.
"I think they (Ferdinand and Vidic) are both very close," Moyes said.
"They played against Premier League opposition in midweek, they both played 90 minutes, so I can't see any reason why they wouldn't be ready to be selected or be involved.
"Danny's had a bit of fluid in his knee, he's trained a few days this week so he's certainly getting much closer to match fitness but he won't travel to Fulham this weekend."